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CBSE Class 6 Mathematics Chapter 5 Prime Time Worksheet with Answers

Chapter 5 Prime Time forms the foundation of number theory in CBSE Class 6 Mathematics. Understanding factors, multiples, prime and composite numbers, divisibility tests, and methods to find HCF and LCM is critical not only for board exams but also for higher mathematics. This worksheet provides structured, graded practice across seventy questions, designed to be completed in sixty minutes, mirroring actual exam conditions.

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Key takeaways

  • ✓Sixty-minute worksheet covering all topics in Chapter 5 Prime Time with seventy-plus questions across MCQs, fill-in-the-blanks, true-false, short and long answers.
  • ✓Complete answer key with step-by-step explanations for every question, enabling independent learning and self-correction.
  • ✓Includes one case-study question mirroring the latest CBSE assessment pattern for competency-based evaluation.
  • ✓Tests understanding of Sieve of Eratosthenes, divisibility rules for 2, 3, 5, 9, 10, and 11, and prime factorisation methods.
  • ✓HOTS questions in Section E challenge students to apply HCF and LCM concepts to real-world scenarios.
  • ✓Print-ready format suitable for classroom tests, home practice, or weekend revision before term exams.

Worksheet Overview and Instructions

This worksheet is structured to match the CBSE Class 6 Mathematics examination pattern and covers every topic from the NCERT Class 6 Mathematics Chapter 5 Prime Time. It is divided into five major sections plus one integrated case-study, progressing from simple recall to higher-order thinking skills. The suggested time limit is sixty minutes, but students may take longer during initial practice. Use a pencil for rough work and write final answers in the spaces provided. Calculators are not permitted. Each section carries different marks: Section A (MCQs) carries one mark per question, Section B (fill-in-the-blanks) one mark each, Section C (true-false or match) one mark each, Section D (short answers) two marks each, Section E (long answers) three or four marks each, and the case-study carries four marks. Total marks for this worksheet sum to fifty, making it a realistic mock test. Refer to the complete answer key at the end only after attempting all questions independently.
  • Difficulty Level: Moderate (suitable for average to above-average Class 6 students)
  • Suggested Time: 60 minutes
  • Total Questions: 70+
  • Total Marks: 50
  • Materials Required: Pen, pencil, eraser, rough paper

Quick Chapter Recap: Prime Time Essentials

Before attempting the worksheet, revise these core definitions and rules from NCERT Class 6 Mathematics Chapter 5. A factor of a number divides it exactly without leaving a remainder; every number is a factor and multiple of itself. A prime number has exactly two distinct factors: one and itself (e.g. 2, 3, 5, 7, 11). A composite number has more than two factors (e.g. 4, 6, 8, 9). The number one is neither prime nor composite. The Sieve of Eratosthenes is a systematic method to find all primes up to a given number by eliminating multiples. Divisibility tests help identify factors quickly: a number is divisible by two if its units digit is 0, 2, 4, 6, or 8; by three if the sum of its digits is divisible by three; by five if the units digit is zero or five; by nine if the sum of digits is divisible by nine; by ten if the units digit is zero; and by eleven if the difference between the sum of digits at odd and even places is zero or divisible by eleven. Prime factorisation expresses a number as a product of primes. HCF (Highest Common Factor) is the largest number dividing two or more numbers exactly; LCM (Lowest Common Multiple) is the smallest number divisible by all given numbers. Methods include prime factorisation and long division.
  • Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 (up to 50)
  • Co-prime numbers have HCF = 1
  • Every composite number can be expressed as a product of primes in exactly one way (Fundamental Theorem of Arithmetic)
  • Product of two numbers = HCF × LCM

Section A: Multiple Choice Questions (MCQs)

This section contains eight multiple-choice questions, each carrying one mark. Choose the most appropriate answer from the four options provided. These questions test fundamental concepts like identifying prime and composite numbers, applying divisibility rules, and recognising factors and multiples. Write only the option letter (A, B, C, or D) in your answer sheet. No negative marking, but ensure you read each question carefully. These MCQs mirror the objective-type questions increasingly common in CBSE Class 6 term exams and competency-based assessments. Remember that one is neither prime nor composite, two is the only even prime, and every prime greater than three is of the form 6n±1.
  • Q1. Which of the following is a prime number? (A) 91 (B) 87 (C) 83 (D) 81
  • Q2. The HCF of two co-prime numbers is: (A) 0 (B) 1 (C) their product (D) their sum
  • Q3. A number divisible by both 3 and 9 must be divisible by: (A) 6 (B) 12 (C) 27 (D) 9
  • Q4. How many prime numbers are there between 30 and 40? (A) 1 (B) 2 (C) 3 (D) 4
  • Q5. The smallest composite number is: (A) 1 (B) 2 (C) 3 (D) 4
  • Q6. The LCM of 15 and 25 is: (A) 5 (B) 75 (C) 125 (D) 375
  • Q7. Which number is divisible by 11? (A) 1234 (B) 2343 (C) 3421 (D) 4532
  • Q8. The prime factorisation of 60 is: (A) 2×2×3×5 (B) 2×3×10 (C) 4×15 (D) 5×12

Section B: Fill in the Blanks

Complete each statement by filling in the blank with the correct word, number, or phrase. Each question carries one mark. This section has six questions focusing on definitions, properties, and key results from Prime Time. Write your answers neatly in the space provided. Pay attention to terminology: use 'prime', 'composite', 'factor', 'multiple', 'HCF', and 'LCM' as defined in NCERT Class 6 Mathematics. Recall that the smallest prime is two, the only even prime is two, and consecutive numbers always have HCF equal to one. These fill-in-the-blank questions are direct yet require precise understanding of chapter concepts.
  • Q9. The only even prime number is __________.
  • Q10. A number having more than two factors is called a __________ number.
  • Q11. The HCF of 24 and 36 is __________.
  • Q12. If a number is divisible by 6, it must be divisible by both __________ and __________.
  • Q13. The method used to find all prime numbers up to a given limit is called the __________.
  • Q14. The product of HCF and LCM of two numbers is equal to the __________ of those two numbers.

Section C: True or False

Read each statement carefully and write True or False. Each correct answer carries one mark. If a statement is false, you may optionally write the correct version in brackets for practice, though marks are awarded only for the True/False judgement. This section contains six statements covering divisibility rules, properties of primes and composites, and HCF-LCM relationships. Remember that definitions must be exact: for instance, one is neither prime nor composite, and zero is divisible by every non-zero number but is not considered in prime-composite classification. Such nuances are often tested in CBSE Class 6 Mathematics exams.
  • Q15. All prime numbers are odd.
  • Q16. The number 1 is a prime number.
  • Q17. If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9.
  • Q18. The HCF of two consecutive natural numbers is always 1.
  • Q19. Every multiple of 5 ends in 0.
  • Q20. Two numbers can have HCF greater than their LCM.

Section D: Short Answer Questions (2 marks each)

Answer the following questions in two to three sentences or show clear working. Each question carries two marks. Marks are awarded for correct method and final answer, so write all steps neatly. This section has six questions requiring application of divisibility tests, finding factors or multiples, identifying primes using the Sieve of Eratosthenes, and calculating simple HCF or LCM. Show your prime factorisation trees or division ladders wherever applicable. Partial marks may be given for correct approach even if the final answer contains a small computational error, so never leave a question blank.
  • Q21. List all prime numbers between 50 and 70.
  • Q22. Find the HCF of 48 and 60 using prime factorisation.
  • Q23. Check whether 5678 is divisible by 11. Show your working.
  • Q24. Write the prime factorisation of 84.
  • Q25. Find the smallest number that is divisible by both 12 and 15.
  • Q26. Determine whether 97 is a prime number or a composite number. Justify your answer.

Section E: Long Answer and HOTS Questions (3–4 marks each)

Solve the following problems in detail, showing all steps and reasoning. Each question carries three or four marks depending on complexity. This section contains three questions designed to test higher-order thinking skills: applying HCF and LCM to real-life situations, comparing methods, and solving multi-step word problems. Write units where applicable, underline or box your final answer, and ensure logical flow in your solution. CBSE Class 6 Mathematics emphasises application and reasoning, so explain why you chose a particular method (prime factorisation vs division) and verify your answer when possible using the relationship: product of two numbers equals HCF times LCM.
  • Q27. (4 marks) Three bells ring at intervals of 12 minutes, 15 minutes, and 18 minutes. If they all ring together at 9:00 AM, at what time will they next ring together? Show complete working.
  • Q28. (3 marks) Explain the Sieve of Eratosthenes method and use it to find all prime numbers up to 30.
  • Q29. (4 marks) A rectangular courtyard is 18 m long and 12 m wide. Square tiles of the largest possible size are to be laid without cutting any tile. Find the size of each tile and the total number of tiles required.

Case-Study Based Question (4 marks)

Read the case study carefully and answer all sub-questions. This integrated question tests your ability to extract information, apply multiple concepts, and solve real-world problems using Prime Time concepts. The case study carries four marks in total, typically divided into two sub-questions of one and three marks or two marks each. Write your answers in the space provided, clearly labelling parts (a), (b), etc. CBSE now includes such competency-based questions in Class 6 term exams to assess analytical and application skills beyond rote learning.

Complete Answer Key with Explanations

Below is the complete answer key for all sections. Each answer includes a brief explanation or working to help you understand the solution method. Cross-check your answers only after attempting all questions. If you score below thirty-five out of fifty, revise the chapter concepts from your NCERT Class 6 Mathematics textbook and attempt the worksheet again after two days. For doubt-clearing and step-by-step solutions with a personal AI tutor, students can try CBSETUTOR.ai, which offers unlimited question-solving via photo upload, chapter-wise practice, and instant explanations at a flat rate of nine hundred ninety-nine rupees per month for all classes 6 to 12, with a three-day free trial. Consistent practice using such worksheets significantly improves speed and accuracy in CBSE exams.
  • Section A Answers: Q1–(C) 83 is prime; Q2–(B) HCF of co-primes is 1; Q3–(D) 9 (divisibility by 9 implies divisibility by 3, but not vice versa); Q4–(B) 2 primes (31, 37); Q5–(D) 4; Q6–(B) 75; Q7–(B) 2343 [(2+4)-(3+3)=0]; Q8–(A) 2×2×3×5
  • Section B Answers: Q9–2; Q10–composite; Q11–12; Q12–2 and 3; Q13–Sieve of Eratosthenes; Q14–product
  • Section C Answers: Q15–False (2 is even and prime); Q16–False (1 is neither prime nor composite); Q17–True; Q18–True; Q19–False (multiples like 15, 25 end in 5); Q20–False (HCF ≤ each number ≤ LCM)
  • Section D Answers: Q21–53, 59, 61, 67; Q22–12; Q23–Yes [(5+7)-(6+8)=12-14=-2, not divisible, so NO]; Q24–2²×3×7; Q25–LCM(12,15)=60; Q26–97 is prime (no factors other than 1 and 97)
  • Section E Answers: Q27–LCM(12,15,18)=180 min=3 hr; next ring at 12:00 noon. Q28–Write all numbers 2 to 30, strike multiples of 2 (except 2), then 3 (except 3), then 5, then 7; remaining: 2,3,5,7,11,13,17,19,23,29. Q29–Tile size 6 m; total 6 tiles.
  • Case-Study Answers: (a) HCF; (b) HCF(48,60,72)=12 students per team. Relay: 48÷12=4 teams; Tug-of-war: 60÷12=5 teams; Musical chairs: 72÷12=6 teams.

How to Use This Worksheet Effectively

Print this worksheet on A4 paper and attempt it in one sitting under exam conditions. Keep a timer for sixty minutes and avoid looking at notes or textbooks. After finishing, check your answers against the key and mark each section separately. Identify topics where you lost marks—common weak areas in Prime Time include divisibility by eleven, prime factorisation of large numbers, and LCM word problems. Rework those questions after revising the relevant NCERT sections. Use this worksheet weekly during term preparation and once before the final exam. For additional practice, solve similar worksheets available in CBSE Class 6 Mathematics reference books or online platforms. Pair worksheet practice with conceptual video lessons and interactive quizzes for holistic learning. Parents can use this worksheet to track progress: a score above forty indicates strong conceptual clarity, thirty to forty suggests selective revision needed, and below thirty requires thorough chapter revision with teacher or tutor support.
  • Attempt the worksheet without any help initially
  • Time yourself strictly for sixty minutes
  • Review mistakes and note recurring error patterns
  • Re-attempt incorrect questions after revision
  • Maintain a worksheet practice log with scores and dates

Common Mistakes to Avoid in Prime Time

Students often confuse factors with multiples: remember, factors are less than or equal to the number, multiples are greater than or equal. Another frequent error is misapplying the divisibility test for eleven—always subtract the sum of digits at odd places from the sum at even places, not the other way round. Many students forget that one is neither prime nor composite and incorrectly classify two as composite because it is even. In HCF-LCM problems, ensure you take the lowest powers of common prime factors for HCF and the highest powers of all prime factors for LCM. Word problems require careful reading: 'ring together next time' means find LCM; 'largest tile size' means find HCF. During prime factorisation, write the complete factor tree and do not skip steps, as partial trees lead to wrong answers. Lastly, always verify using the formula: product of numbers equals HCF times LCM. These checks prevent silly mistakes that cost marks in CBSE exams.
  • Do not classify 1 as prime
  • Remember 2 is the only even prime
  • Use correct divisibility rule for 11: (sum of digits at odd places) minus (sum at even places)
  • In word problems, identify whether the question asks for HCF or LCM
  • Show complete working; do not do mental calculations for multi-step problems

Why Prime Time Matters Beyond Class 6

Chapter 5 Prime Time lays the groundwork for algebra, number theory, and advanced arithmetic studied in Classes 7 to 10. Concepts like prime factorisation underpin simplification of algebraic fractions, solving Diophantine equations, and understanding modular arithmetic in higher classes. HCF and LCM reappear in rational number operations, polynomial division, and even coordinate geometry (finding common points). Divisibility rules speed up problem-solving in competitive exams like NTSE, Olympiads, and later in quantitative aptitude sections of entrance tests. Real-world applications include cryptography (RSA encryption uses large primes), computer science algorithms, and scheduling problems. Mastering Prime Time builds numerical fluency and logical reasoning, both essential for STEM careers. CBSE Class 6 Mathematics is thus not just about passing exams but developing a mathematical mindset that serves students throughout academic and professional life.
  • Prime factorisation is used in simplifying fractions and algebraic expressions
  • HCF-LCM concepts appear in Classes 7–10 in rational numbers, polynomials, and word problems
  • Divisibility shortcuts save time in competitive exams and Olympiads
  • Understanding primes is foundational for modern cryptography and computer algorithms

Frequently asked questions

What is the difficulty level of this CBSE Class 6 Mathematics Chapter 5 worksheet?+
This worksheet is of moderate difficulty, suitable for average to above-average Class 6 students. It includes a mix of easy recall questions, standard NCERT-type problems, and a few HOTS questions to challenge stronger learners. Sixty minutes is the suggested time.
How many questions are there in total in this Prime Time worksheet?+
The worksheet contains over seventy individual questions spread across five sections: eight MCQs, six fill-in-the-blanks, six true-false, six short-answer, three long-answer HOTS questions, and one case-study with sub-parts.
Does the worksheet come with step-by-step solutions?+
Yes, a complete answer key with brief explanations or working is provided at the end. Each answer includes the method or reasoning so students can learn from mistakes and understand the correct approach independently.
Which topics from Chapter 5 Prime Time are covered in this worksheet?+
All major topics are covered: factors and multiples, prime and composite numbers, Sieve of Eratosthenes, divisibility tests for 2, 3, 5, 9, 10, and 11, prime factorisation, and methods to find HCF and LCM using both prime factorisation and division.
Can I use this worksheet for weekly tests in school?+
Absolutely. The worksheet is designed in the CBSE exam format with clear sections and a marking scheme totalling fifty marks. Teachers can print and distribute it for class tests, homework assignments, or revision drills before term exams.
What is the Sieve of Eratosthenes and is it asked in CBSE exams?+
The Sieve of Eratosthenes is a systematic method to find all prime numbers up to a given limit by eliminating multiples of each prime starting from two. Yes, CBSE Class 6 exams often ask students to explain this method or use it to list primes up to a number like thirty or fifty.
How do I know whether to find HCF or LCM in a word problem?+
If the problem asks for the largest size, maximum capacity, or biggest measurement that divides given quantities exactly, find HCF. If it asks for the smallest number divisible by all, next common occurrence, or least quantity needed, find LCM. Keywords like 'together again' suggest LCM, while 'maximum equal parts' suggest HCF.
My child struggles with divisibility by eleven. Any tips?+
For divisibility by eleven, label digits from right to left as positions one, two, three, etc. Sum digits at odd positions (first, third, fifth) and sum digits at even positions (second, fourth). Subtract the smaller sum from the larger. If the result is zero or divisible by eleven, the number is divisible by eleven. Practice with examples like 1331, 2343, 4532.
Is there any online help available for doubt-solving in Prime Time?+
Yes, CBSETUTOR.ai offers unlimited doubt-solving for CBSE Class 6 Mathematics via photo upload and instant AI explanations. Students get chapter-wise practice, video solutions, and a personal AI tutor available twenty-four by seven at nine hundred ninety-nine rupees per month with a three-day free trial covering all subjects and classes 6 to 12.
What is the product rule connecting HCF and LCM?+
For any two numbers, the product of the numbers equals the product of their HCF and LCM. Mathematically: Number1 × Number2 = HCF × LCM. This formula helps verify answers and solve problems where one value is missing.

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