Class 9 Mathematics Chapter 5 Prime Time MCQ: 30 Solved Questions with Answers

The CBSE Class 9 assessment structure has shifted significantly. Under the rationalized 2024–25 curriculum, multiple-choice questions now account for 25–40% of question papers across Mathematics, Science, and other subjects. This shift reflects two pedagogical goals: (1) testing conceptual clarity quickly across wide syllabus coverage, and (2) reducing lengthy calculations to focus on logic and reasoning. In Chapter 5: Prime Time, MCQs test your ability to instantly recognise prime vs composite numbers, apply divisibility rules mentally, factorise numbers into primes, and compute HCF/LCM without long division. Unlike long-answer questions, MCQs reward precision and speed—but only if you avoid common misconceptions. For example, many students confuse prime numbers with odd numbers, or incorrectly apply the divisibility test for 11 (alternating sum vs simple digit sum). The trap lies in partially correct reasoning: you might know that 51 = 3 × 17 (both prime), yet mark it "composite" because 51 itself is composite. MCQ success depends on anchoring your understanding to NCERT definitions and practising under time pressure. This quiz is designed to build both confidence and speed through realistic, exam-style questions.

**Q1.** Which of the following is a prime number? (A) 1 (B) 9 (C) 17 (D) 21 **Answer:** (C) 17 **Reason:** Prime numbers have exactly two factors (1 and the number itself); 17 has no other divisors. **Q2.** What is the smallest prime number? (A) 0 (B) 1 (C) 2 (D) 3 **Answer:** (C) 2 **Reason:** 2 is the only even prime; 1 is neither prime nor composite by NCERT definition. **Q3.** How many factors does 12 have? (A) 2 (B) 3 (C) 6 (D) 12 **Answer:** (C) 6 **Reason:** Factors of 12 are: 1, 2, 3, 4, 6, 12. **Q4.** Which number is divisible by 5? (A) 234 (B) 347 (C) 450 (D) 561 **Answer:** (C) 450 **Reason:** Numbers ending in 0 or 5 are divisible by 5. **Q5.** Is 36 divisible by 3? (A) No (B) Yes (C) Cannot determine (D) Only if even **Answer:** (B) Yes **Reason:** Sum of digits: 3 + 6 = 9, divisible by 3, so 36 is divisible by 3. **Q6.** Which of the following is a composite number? (A) 23 (B) 29 (C) 32 (D) 37 **Answer:** (C) 32 **Reason:** 32 = 2⁵; has factors other than 1 and itself. **Q7.** Is 100 a multiple of 10? (A) No (B) Yes (C) Sometimes (D) Only in multiples **Answer:** (B) Yes **Reason:** 100 = 10 × 10; so 10 divides 100 evenly. **Q8.** What is the divisibility rule for 2? (A) Sum of digits is even (B) Last digit is even (C) Number ends in 2 (D) Number is odd **Answer:** (B) Last digit is even **Reason:** A number is divisible by 2 if its units digit is 0, 2, 4, 6, or 8. **Q9.** Is 84 divisible by both 2 and 3? (A) Yes (B) No (C) Only by 2 (D) Only by 3 **Answer:** (A) Yes **Reason:** 84 is even (divisible by 2) and 8 + 4 = 12 (divisible by 3). **Q10.** Which number is NOT divisible by 10? (A) 120 (B) 250 (C) 305 (D) 400 **Answer:** (C) 305 **Reason:** Numbers divisible by 10 must end in 0; 305 ends in 5.

**Q11.** What is the prime factorisation of 60? (A) 2² × 3 × 5 (B) 2 × 3 × 5² (C) 2 × 3² × 5 (D) 2³ × 3 × 5 **Answer:** (A) 2² × 3 × 5 **Reason:** 60 = 4 × 15 = 2² × 3 × 5. **Q12.** What is the HCF of 24 and 36? (A) 6 (B) 12 (C) 24 (D) 36 **Answer:** (B) 12 **Reason:** Factors of 24: 1,2,3,4,6,8,12,24; Factors of 36: 1,2,3,4,6,9,12,18,36; HCF = 12. **Q13.** What is the LCM of 12 and 18? (A) 6 (B) 18 (C) 36 (D) 72 **Answer:** (C) 36 **Reason:** 12 = 2² × 3; 18 = 2 × 3²; LCM = 2² × 3² = 36. **Q14.** Which number has exactly 3 as a prime factor? (A) 10 (B) 15 (C) 28 (D) 49 **Answer:** (B) 15 **Reason:** 15 = 3 × 5; only 15 contains 3 as a prime factor. **Q15.** If HCF(a, b) = 4 and LCM(a, b) = 48, what is a × b? (A) 12 (B) 48 (C) 96 (D) 192 **Answer:** (D) 192 **Reason:** a × b = HCF(a, b) × LCM(a, b) = 4 × 48 = 192. **Q16.** Is 91 a prime number? (A) Yes (B) No (C) Cannot determine (D) Only if odd **Answer:** (B) No **Reason:** 91 = 7 × 13; has factors other than 1 and itself. **Q17.** What is the prime factorisation of 72? (A) 2³ × 3² (B) 2² × 3³ (C) 2³ × 3³ (D) 2 × 3⁴ **Answer:** (A) 2³ × 3² **Reason:** 72 = 8 × 9 = 2³ × 3². **Q18.** What is the smallest number divisible by both 8 and 12? (A) 24 (B) 32 (C) 48 (D) 96 **Answer:** (A) 24 **Reason:** LCM(8, 12) = 24; 8 = 2³, 12 = 2² × 3; LCM = 2³ × 3 = 24. **Q19.** If the HCF of two numbers is 5, which pair could they be? (A) 10 and 15 (B) 15 and 25 (C) 20 and 30 (D) All of the above **Answer:** (D) All of the above **Reason:** HCF(10,15)=5; HCF(15,25)=5; HCF(20,30)=10 (incorrect—this is a trap). Wait, HCF(20,30)=10, not 5. So (A) and (B) work. **Corrected Answer:** (C) is a trap. Answer is **(A) and (B)** — but since single-select: verify all three: 10,15 → 5; 15,25 → 5; 20,30 → 10. Choose (A) **or** (B). **Q20.** Which of these is NOT a factor of 120? (A) 8 (B) 15 (C) 16 (D) 30 **Answer:** (C) 16 **Reason:** 120 ÷ 16 = 7.5 (not a whole number); 120 = 2³ × 3 × 5; 16 = 2⁴ requires four 2s, but 120 has only three.

**Q21. Assertion–Reason Format:** **Assertion (A):** The number 2,013 is divisible by 3. **Reason (R):** A number is divisible by 3 if the sum of its digits is divisible by 3. (A) Both A and R are true; R explains A. (B) Both true; R does not explain A. (C) A true, R false. (D) A false, R true. **Answer:** (A) **Reason:** Sum of digits: 2 + 0 + 1 + 3 = 6 (divisible by 3); hence A is true. R is the correct rule. **Q22.** Which number satisfies the divisibility test for 11? (A) 4,752 (B) 5,291 (C) 7,436 (D) 8,943 **Answer:** (A) 4,752 **Reason:** Test for 11: alternating sum of digits. 4 − 7 + 5 − 2 = 0 (divisible by 11). **Q23. Assertion–Reason:** **Assertion:** Every even number greater than 2 is composite. **Reason:** Composite numbers have more than two factors. (A) A true, R true; R explains A. (B) A true, R true; R doesn't explain. (C) A true, R false. (D) A false, R true. **Answer:** (A) **Reason:** All even numbers > 2 are divisible by 2 and themselves (at least 2 factors), hence composite. R correctly explains why. **Q24.** If p is a prime number and p divides a × b, then: (A) p must divide a or p must divide b. (B) p divides both a and b. (C) p divides a + b. (D) p cannot divide either. **Answer:** (A) **Reason:** This is Euclid's Lemma (NCERT Class 9 Number Theory); a core property of primes. **Q25. Assertion–Reason:** **Assertion:** 1 is neither prime nor composite. **Reason:** Prime numbers must have exactly two distinct factors. (A) Both true; R explains A. (B) Both true; R doesn't explain. (C) A true, R false. (D) Both false. **Answer:** (A) **Reason:** By NCERT definition, 1 has only one factor (itself); primes require exactly two. R correctly explains A. **Q26.** The sum of two prime numbers is 30. If one prime is 13, what is the other? (A) 15 (B) 17 (C) 19 (D) 21 **Answer:** (B) 17 **Reason:** 30 − 13 = 17; 17 is prime (only divisors: 1, 17). **Q27. Assertion–Reason:** **Assertion:** The LCM of two coprime numbers equals their product. **Reason:** Coprime numbers have HCF = 1. (A) A true, R true; R explains A. (B) A true, R true; R doesn't explain. (C) A true, R false. (D) A false, R true. **Answer:** (A) **Reason:** If HCF(a,b)=1, then LCM(a,b)=a×b (from formula a×b=HCF×LCM). R explains A. **Q28.** Using the Sieve of Eratosthenes, how many primes are there between 1 and 30? (A) 10 (B) 9 (C) 11 (D) 8 **Answer:** (A) 10 **Reason:** Primes ≤ 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (exactly 10). **Q29.** If n = 2² × 3 × 5, how many factors does n have? (A) 6 (B) 10 (C) 12 (D) 15 **Answer:** (C) 12 **Reason:** Number of factors = (2+1)(1+1)(1+1) = 3 × 2 × 2 = 12 (using exponent formula). **Q30. Assertion–Reason:** **Assertion:** 9,999 is divisible by 9. **Reason:** The divisibility rule for 9 is the same as for 3 (digit sum). (A) Both true; R explains A. (B) Both true; R doesn't explain. (C) A true, R false. (D) A false, R true. **Answer:** (A) **Reason:** Sum of digits: 9+9+9+9=36 (divisible by 9). R states the correct rule (divisibility by 9 uses digit sum, just as 3 does).

MCQs in Chapter 5 exploit predictable misconceptions. Understanding these traps will save you marks: **Trap 1: Confusing Prime with Odd.** Many students mark odd numbers like 9, 15, 21, or 25 as prime because they're not even. Reality: 9 = 3², 15 = 3×5, 21 = 3×7, 25 = 5². **Defence:** Always factorise; if you find two factors besides 1, it's composite. **Trap 2: Thinking 1 is Prime.** NCERT explicitly states 1 is neither prime nor composite. Older textbooks sometimes included it, but current CBSE does not. **Defence:** Memorise the definition: a prime has *exactly* two factors; 1 has only one. **Trap 3: Divisibility Rule for 11 Errors.** Students often sum all digits (like the rule for 3) or subtract all digits. The correct rule: **alternating sum** (starting from the right). Example: 5,291 → 1 − 9 + 2 − 5 = −11 (divisible by 11). **Defence:** Practice the alternating sum pattern on 3–4 examples until automatic. **Trap 4: Forgetting HCF/LCM Relationship.** Students compute HCF and LCM separately, forgetting that **a × b = HCF(a,b) × LCM(a,b)**. This identity rescues you in questions where one is given. **Defence:** Write the formula on your rough sheet immediately after reading such questions. **Trap 5: Misapplying the Factor Counting Formula.** For n = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ, the number of factors is **(a₁+1)(a₂+1)...(aₖ+1)**, not just adding exponents. Example: 72 = 2³ × 3² has (3+1)(2+1) = 12 factors, not 5. **Defence:** Write the formula out; practice on 3–4 examples. **Trap 6: Assuming All Odd Numbers > 2 Are Prime.** Composites like 9, 15, 21, 25, 27, 33, 35, 39, 45, 49 are all odd. **Defence:** When a number looks prime, mentally check divisibility by small primes: is it divisible by 3 (digit sum rule)? By 5 (ends in 5)? By 7 (trial division)? **Trap 7: Confusing Factors with Multiples.** Factors divide *into* a number; multiples are produced *by* a number. Example: 3 is a factor of 12, and 12 is a multiple of 3. **Defence:** Use the phrase "divides evenly into" for factors. **Actionable Checklist:** Before clicking your answer, ask: (1) Did I factorise correctly? (2) Is 1 really prime? (3) Did I apply the *alternating* sum for 11? (4) Did I use the (a₁+1)(a₂+1)... formula for factor count? (5) Did I verify a × b = HCF × LCM?

In a 2-hour exam with 30 MCQs (30 marks for Chapter 5 questions), you have roughly 4 minutes per question including reading. Speed without accuracy is worthless; here's a battle-tested approach: **Phase 1: Scanning (2 minutes for 30 Qs).** Before you write anything, scan all questions. Mark them: ★ (confident), ◐ (medium), ✗ (unsure). This psychological priming activates dormant knowledge. **Phase 2: Low-Hanging Fruit (8–10 minutes).** Attack all ★ questions first. These are rapid wins—divisibility tests, basic factorisation, recognising primes. Invest 1–2 minutes per question, no more. Move on. **Phase 3: Medium Difficulty (10–12 minutes).** Tackle ◐ questions: HCF/LCM, factor-count formulas, assertion–reason pairs requiring two-step logic. Allocate 2–3 minutes per question. If stuck after 2 minutes, skip and return. **Phase 4: Hard Questions (5 minutes max per question).** Revisit ✗ questions only after completing all others. Assertion–Reason MCQs need careful reading: (1) Is the assertion true? (2) Is the reason true? (3) Does reason logically explain assertion? Don't rush this. **Phase 5: Review (remaining time).** Revisit your answers *only if time remains*. Common catches: re-reading a divisibility test (did you apply alternating sum correctly for 11?), rechecking sign errors in HCF/LCM products, verifying digit sums for rules 3 and 9. **Exam-Day Hacks:** • Write divisibility rules as a mini-reference on your rough sheet immediately. • For HCF/LCM, always verify using a × b = HCF × LCM before finalising. • If an Assertion–Reason question confuses you, ignore the "relationship" and just verify each statement independently first. • For factor-count questions, always factorise completely, then apply (a₁+1)(a₂+1)..., never guess. • If you're unsure between two options, eliminate the obvious distractors (e.g., 1 is never prime; 16 never divides 120). **Mental Stamina.** Chapter 5 MCQs are conceptual, not calculation-heavy. Your brain may fatigue from rapid-fire thinking, not arithmetic. After answering 10 questions, take 30 seconds: breathe, roll your shoulders, refocus. Start a 3-day free trial at cbsetutor.ai to practise full-length mock exams with real timing and see your weak spots instantly.

Lock these into memory before your exam: **Divisibility Rules (NCERT Ch. 5):** • **By 2:** Last digit is 0, 2, 4, 6, or 8. • **By 3:** Sum of all digits is divisible by 3. • **By 5:** Last digit is 0 or 5. • **By 9:** Sum of all digits is divisible by 9. • **By 10:** Last digit is 0. • **By 11:** Alternating sum of digits (from right) is divisible by 11. Example: 5,291 → 1 − 9 + 2 − 5 = −11 ✓. **Prime Factorisation & Factors:** • If n = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ, then **Number of Factors = (a₁+1)(a₂+1)...(aₖ+1)**. • Example: 60 = 2² × 3 × 5 → Factors = (2+1)(1+1)(1+1) = 12. **HCF & LCM (NCERT definitions):** • **HCF (Highest Common Factor):** Largest number dividing both. • **LCM (Least Common Multiple):** Smallest number divisible by both. • **Key Formula:** **a × b = HCF(a, b) × LCM(a, b)**. • **Coprime Numbers:** HCF = 1; hence LCM(a,b) = a × b. **Sieve of Eratosthenes:** Systematic method to find all primes up to n by iteratively marking multiples of each prime as composite. Primes ≤ 30: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}. **Definitions (NCERT, must be exact):** • **Prime:** Natural number > 1 with exactly two factors (1 and itself). • **Composite:** Natural number > 1 with more than two factors. • **Neither:** 1 is neither prime nor composite (CBSE, 2024–25). • **Factor:** Divides a number evenly (remainder = 0). • **Multiple:** Produced by multiplying a number by another natural number. **Euclid's Lemma (useful for hard questions):** If prime p divides a × b, then p divides a OR p divides b (or both).