Prime Time — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Prime Time" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Prime Time" — 8 important questions with detailed answers for CBSE board exam prepa…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 6 Mathematics — Prime Time. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Prime Time — All 8 Questions Solved
Q1. What is the difference between a prime number and a composite number?
Step 1: Define a prime number
A prime number is a number greater than 1 that has exactly two factors: 1 and itself
Example: 7 is prime because only 1 and 7 divide it evenly
Factors of 7: 1, 7
Step 2: Define a composite number
A composite number is a number greater than 1 that has more than two factors
Example: 8 is composite because 1, 2, 4, and 8 all divide it evenly
Factors of 8: 1, 2, 4, 8
Step 3: Note about 1
1 is neither prime nor composite (it has only one factor: itself)
Step 4: Compare
Prime: exactly 2 factors (1 and itself)
Composite: more than 2 factors
Answer: A prime number has exactly 2 factors (1 and itself). A composite number has more than 2 factors. Example: 5 is prime (factors: 1, 5). 6 is composite (factors: 1, 2, 3, 6).
Q2. List all prime numbers between 10 and 30.
A prime number has exactly two factors: 1 and itself.
Step 1: Check each number from 10 to 30
10: factors are 1, 2, 5, 10 → composite (more than 2 factors)
11: factors are 1, 11 → prime ✓
12: factors are 1, 2, 3, 4, 6, 12 → composite
13: factors are 1, 13 → prime ✓
14: factors are 1, 2, 7, 14 → composite
15: factors are 1, 3, 5, 15 → composite
16: factors are 1, 2, 4, 8, 16 → composite
17: factors are 1, 17 → prime ✓
18: factors are 1, 2, 3, 6, 9, 18 → composite
19: factors are 1, 19 → prime ✓
20: factors are 1, 2, 4, 5, 10, 20 → composite
21: factors are 1, 3, 7, 21 → composite
22: factors are 1, 2, 11, 22 → composite
23: factors are 1, 23 → prime ✓
24: factors are 1, 2, 3, 4, 6, 8, 12, 24 → composite
25: factors are 1, 5, 25 → composite
26: factors are 1, 2, 13, 26 → composite
27: factors are 1, 3, 9, 27 → composite
28: factors are 1, 2, 4, 7, 14, 28 → composite
29: factors are 1, 29 → prime ✓
30: factors are 1, 2, 3, 5, 6, 10, 15, 30 → composite
Step 2: List all primes found
Answer: 11, 13, 17, 19, 23, 29
Q3. Find all factors of 36.
Factors are numbers that divide evenly into another number (with no remainder).
Step 1: Test each number starting from 1
36 ÷ 1 = 36 → 1 and 36 are factors
36 ÷ 2 = 18 → 2 and 18 are factors
36 ÷ 3 = 12 → 3 and 12 are factors
36 ÷ 4 = 9 → 4 and 9 are factors
36 ÷ 5 = 7.2 → 5 is not a factor
36 ÷ 6 = 6 → 6 is a factor
Step 2: Continue up to the square root
We only need to check up to √36 = 6
Step 3: List all factors in order
Step 4: Organize
1, 2, 3, 4, 6, 9, 12, 18, 36
Answer: The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36 (Total: 9 factors)
Q4. Write the first five multiples of 7.
Multiples are numbers you get when you multiply a number by 1, 2, 3, 4, ...
Step 1: Multiply 7 by 1
7 × 1 = 7 (1st multiple)
Step 2: Multiply 7 by 2
7 × 2 = 14 (2nd multiple)
Step 3: Multiply 7 by 3
7 × 3 = 21 (3rd multiple)
Step 4: Multiply 7 by 4
7 × 4 = 28 (4th multiple)
Step 5: Multiply 7 by 5
7 × 5 = 35 (5th multiple)
Answer: The first five multiples of 7 are: 7, 14, 21, 28, 35
Q5. Find the HCF of 12 and 18 using the listing method.
The HCF (Highest Common Factor) is the largest number that divides both numbers.
Step 1: List all factors of 12
Factors of 12: 1, 2, 3, 4, 6, 12
Step 2: List all factors of 18
Factors of 18: 1, 2, 3, 6, 9, 18
Step 3: Identify common factors (factors in both lists)
Common factors: 1, 2, 3, 6
Step 4: Find the highest common factor
HCF = 6
Step 5: Verify
12 ÷ 6 = 2 ✓
18 ÷ 6 = 3 ✓
Answer: The HCF of 12 and 18 is 6
Q6. Is 1 a prime number? Explain why or why not.
Step 1: Recall the definition of a prime number
A prime number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself
Step 2: Check the factors of 1
The only factor of 1 is 1 itself
1 has only 1 factor (itself), not 2 factors
Step 3: Apply the definition
Since 1 has only one factor (not two), it does not fit the definition of a prime number
Step 4: Also note
1 also does not fit the definition of a composite number (which needs more than 2 factors)
So 1 is in a special category: neither prime nor composite
Answer: No, 1 is not a prime number because it has only one factor (itself), while prime numbers must have exactly two factors: 1 and the number itself.
Q7. Find the LCM of 4 and 6 using the listing method.
The LCM (Lowest Common Multiple) is the smallest positive number that is a multiple of both numbers.
Step 1: List multiples of 4
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Step 2: List multiples of 6
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Step 3: Find common multiples (multiples in both lists)
Common multiples: 12, 24, 36, ...
Step 4: Identify the lowest common multiple
The smallest number in the common multiples list is 12
LCM = 12
Step 5: Verify
12 ÷ 4 = 3 ✓
12 ÷ 6 = 2 ✓
Answer: The LCM of 4 and 6 is 12
Q8. Use divisibility rules to check if 144 is divisible by both 4 and 9.
Step 1: Check divisibility by 4
Rule: A number is divisible by 4 if the last two digits form a number divisible by 4
144: last two digits are 44
Is 44 divisible by 4?
44 ÷ 4 = 11 ✓
Yes, 144 is divisible by 4
Step 2: Check divisibility by 9
Rule: A number is divisible by 9 if the sum of its digits is divisible by 9
144: sum of digits = 1 + 4 + 4 = 9
Is 9 divisible by 9?
9 ÷ 9 = 1 ✓
Yes, 144 is divisible by 9
Step 3: Verify by actual division
144 ÷ 4 = 36 ✓
144 ÷ 9 = 16 ✓
Answer: Yes, 144 is divisible by both 4 and 9. Using divisibility rules: the last two digits (44) are divisible by 4, and the sum of digits (1+4+4=9) is divisible by 9.
Prime Time — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. Which of the following best describes a prime number?
- A. A number with exactly two factors (1 and itself)
- B. A number with more than two factors
- C. A number that is only divisible by 1
- D. A number that is always odd
Answer: A. A number with exactly two factors (1 and itself) — A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself, meaning it has exactly two factors.
MCQ 2. What is the smallest prime number?
- A. 0
- B. 1
- C. 2
- D. 3
Answer: C. 2 — The number 2 is the smallest prime number because it is greater than 1 and has only two factors: 1 and 2.
MCQ 3. Which of the following is the only even prime number?
- A. 2
- B. 4
- C. 6
- D. 8
Answer: A. 2 — All even numbers greater than 2 are divisible by 2 and themselves, and also by 1, making them composite. Hence, 2 is the only even prime number.
MCQ 4. From the given numbers, identify the prime number:
- A. 9
- B. 15
- C. 21
- D. 13
Answer: D. 13 — The number 13 has only two factors, 1 and 13, making it a prime number. 9, 15, and 21 have more than two factors.
MCQ 5. What is the smallest composite number?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: D. 4 — A composite number is a natural number that has more than two factors. The number 4 has factors 1, 2, and 4, making it the smallest composite number.
MCQ 6. Is the number 1 a prime number, a composite number, or neither?
- A. Prime
- B. Composite
- C. Neither prime nor composite
- D. Both prime and composite
Answer: C. Neither prime nor composite — A prime number has exactly two factors, and a composite number has more than two factors. The number 1 has only one factor (itself), so it is neither prime nor composite.
MCQ 7. How many prime numbers are there between 20 and 30?
- A. 2
- B. 3
- C. 4
- D. 5
Answer: A. 2 — The prime numbers between 20 and 30 are 23 and 29. There are 2 such prime numbers.
MCQ 8. What is the prime factorization of 36?
- A. 2 x 3 x 6
- B. 2 x 2 x 3 x 3
- C. 4 x 9
- D. 2 x 18
Answer: B. 2 x 2 x 3 x 3 — Prime factorization involves expressing a number as a product of its prime factors. For 36, it is 2 x 2 x 3 x 3.
MCQ 9. What is the sum of the first three prime numbers?
- A. 6
- B. 8
- C. 10
- D. 12
Answer: C. 10 — The first three prime numbers are 2, 3, and 5. Their sum is 2 + 3 + 5 = 10.
MCQ 10. Which of the following pairs represents twin primes?
- A. (3, 5)
- B. (7, 11)
- C. (13, 17)
- D. (19, 23)
Answer: A. (3, 5) — Twin primes are a pair of prime numbers that differ by 2. From the options, (3, 5) is a pair of twin primes as both are prime and 5 - 3 = 2.
MCQ 11. Using prime factorization, find the Highest Common Factor (HCF) of 12 and 18.
- A. 2
- B. 3
- C. 6
- D. 12
Answer: C. 6 — Prime factorization of 12 is 2 x 2 x 3. Prime factorization of 18 is 2 x 3 x 3. The common prime factors are 2 and 3, so HCF = 2 x 3 = 6.
MCQ 12. Using prime factorization, find the Least Common Multiple (LCM) of 8 and 12.
- A. 4
- B. 12
- C. 24
- D. 48
Answer: C. 24 — Prime factorization of 8 is 2 x 2 x 2. Prime factorization of 12 is 2 x 2 x 3. The LCM is found by taking the highest powers of all prime factors involved: 2^3 x 3^1 = 8 x 3 = 24.
MCQ 13. Which of the following numbers is composite because it is divisible by 5?
- A. 17
- B. 23
- C. 35
- D. 41
Answer: C. 35 — A composite number has more than two factors. The number 35 is divisible by 1, 5, 7, and 35, making it a composite number.
MCQ 14. How many prime numbers are there between 40 and 60?
- A. 4
- B. 5
- C. 6
- D. 7
Answer: B. 5 — The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59. There are 5 such prime numbers.
MCQ 15. Two bells ring at intervals of 8 minutes and 12 minutes respectively. If they ring together at 9:00 AM, when will they next ring together?
- A. 9:16 AM
- B. 9:20 AM
- C. 9:24 AM
- D. 9:36 AM
Answer: C. 9:24 AM — To find when they next ring together, we need to find the LCM of 8 and 12. The LCM of 8 and 12 is 24. So, they will next ring together after 24 minutes, which is 9:24 AM.
MCQ 16. Which of the following numbers is a prime number?
- A. 4
- B. 9
- C. 13
- D. 15
Answer: C. 13 — A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. 13 only has factors 1 and 13.
MCQ 17. Which of the following is a multiple of 7?
- A. 24
- B. 35
- C. 40
- D. 52
Answer: B. 35 — A multiple of 7 is a number that can be divided by 7 without leaving a remainder. 35 divided by 7 is 5.
MCQ 18. How many composite numbers are there between 20 and 30 (excluding 20 and 30)?
- A. 5
- B. 6
- C. 7
- D. 8
Answer: C. 7 — The numbers between 20 and 30 are 21, 22, 23, 24, 25, 26, 27, 28, 29. The prime numbers are 23 and 29. The composite numbers are 21, 22, 24, 25, 26, 27, 28, which are 7 in total.
MCQ 19. The number 1 is:
- A. A prime number
- B. A composite number
- C. Neither prime nor composite
- D. An even number
Answer: C. Neither prime nor composite — A prime number has exactly two factors, and a composite number has more than two factors. The number 1 has only one factor (itself), so it is neither prime nor composite.
MCQ 20. Which of the following numbers is divisible by 5?
- A. 123
- B. 456
- C. 780
- D. 912
Answer: C. 780 — A number is divisible by 5 if its last digit is either 0 or 5. 780 ends with 0, making it divisible by 5.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.