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About Prime Factors & Divisibility — Class 6 IB

Use prime factorization, HCF, and LCM to solve number problems. This topic is part of the IB Class 6 mathematics syllabus (chapter: Unit 12). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Prime Factors & Divisibility — solved examples for Class 6 IB

Example 1easy

Which of these numbers is a prime number?
  1. A)12
  2. B)15
  3. C)17
  4. D)21

Step-by-step solution

  1. Check each number:
  2. 12 = 2 × 6, so not prime
  3. 15 = 3 × 5, so not prime
  4. 17 has no factors other than 1 and 17, so it is prime
  5. 21 = 3 × 7, so not prime

Answer: 17

Example 2medium

Express 72 as a product of its prime factors.
  1. A)23×322^3 \times 3^2
  2. B)22×332^2 \times 3^3
  3. C)23×92^3 \times 9
  4. D)8×98 \times 9

Step-by-step solution

  1. 72 = 2 × 36
  2. 36 = 2 × 18
  3. 18 = 2 × 9
  4. 9 = 3 × 3
  5. So 72 = 2 × 2 × 2 × 3 × 3
    72=23×3272 = 2^3 \times 3^2

Answer: 23×322^3 \times 3^2

Example 3hard

Express 360 as a product of its prime factors.
  1. A)23×32×52^3 \times 3^2 \times 5
  2. B)22×32×102^2 \times 3^2 \times 10
  3. C)23×452^3 \times 45
  4. D)22×3×522^2 \times 3 \times 5^2

Step-by-step solution

  1. 360 = 2 × 180
  2. 180 = 2 × 90
  3. 90 = 2 × 45
  4. 45 = 3 × 15
  5. 15 = 3 × 5
  6. So 360 = 2³ × 3² × 5
    360=23×32×5360 = 2^3 \times 3^2 \times 5

Answer: 23×32×52^3 \times 3^2 \times 5

Practice questions on Prime Factors & Divisibility

  1. Q1.easy

    What is the smallest prime number?
    1. A)0
    2. B)1
    3. C)2
    4. D)3
    Show answer

    Answer: 2

    Hint: Remember, 1 is NOT a prime number.

  2. Q2.easy

    Is 24 divisible by 3?
    1. A)Yes, because 2 + 4 = 6 which is divisible by 3
    2. B)No, because 24 is even
    3. C)Yes, because 24 ends in 4
    4. D)No, because 24 is not a multiple of 9
    Show answer

    Answer: Yes, because 2 + 4 = 6 which is divisible by 3

    Hint: A number is divisible by 3 if the sum of its digits is divisible by 3.

  3. Q3.easy

    List all the factors of 18.
    1. A)1, 2, 3, 6, 9, 18
    2. B)1, 2, 3, 9, 18
    3. C)2, 3, 6, 9
    4. D)1, 2, 6, 18
    Show answer

    Answer: 1, 2, 3, 6, 9, 18

    Hint: Check every number from 1 up to 18 to see if it divides 18 evenly.

  4. Q4.medium

    Find the HCF of 24 and 36.
    1. A)6
    2. B)8
    3. C)12
    4. D)18
    Show answer

    Answer: 12

    Hint: Write each as a product of primes, then multiply the common prime factors.

  5. Q5.medium

    Find the LCM of 8 and 12.
    1. A)24
    2. B)48
    3. C)96
    4. D)4
    Show answer

    Answer: 24

    Hint: Write each as a product of primes, then take the highest power of each prime.

  6. Q6.medium

    A number is divisible by 6 if it is divisible by:
    1. A)2 and 3
    2. B)2 and 6
    3. C)3 and 6
    4. D)2 only
    Show answer

    Answer: 2 and 3

    Hint: 6 = 2 × 3, so divisibility by 6 requires both conditions.

  7. Q7.hard

    Find the HCF of 84 and 126.
    1. A)14
    2. B)21
    3. C)42
    4. D)7
    Show answer

    Answer: 42

    Hint: Prime factorise both numbers first.

  8. Q8.hard

    Find the LCM of 15 and 20.
    1. A)30
    2. B)60
    3. C)100
    4. D)300
    Show answer

    Answer: 60

    Hint: 15 = 3 × 5 and 20 = 2² × 5. Take the highest power of each prime.

  9. Q9.hard

    What is the smallest number that has exactly 6 factors?
    1. A)12
    2. B)18
    3. C)20
    4. D)28
    Show answer

    Answer: 12

    Hint: 6 factors means (a+1)(b+1) = 6 for prime factorisation pa×qbp^a \times q^b. Try different combinations.

These are 9 of the 60 questions available for Prime Factors & Divisibility. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.