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Prime factorization

Write whole numbers as products of prime factors.

Practice + answer key · 2 pages

Worksheet settings8 questions · 2 columns · A4
Starting-number range

Choose the integers to factor into primes.

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mathsprig-1
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Prime factorizationPrime factorization. Practice. Write 15 as a product of prime factors. Write 87 as a product of prime factors. Write 38 as a product of prime factors. Write 109 as a product of prime factors. Write 29 as a product of prime factors. Write 51 as a product of prime factors. Write 105 as a product of prime factors. Write 74 as a product of prime factors.Name __________________________Date _______________Prime factorizationWrite each number as a product of prime factors.Worked exampleWrite 84 as a product of prime factors. → 2 × 2 × 3 × 784 ÷ 2 = 42, then 42 ÷ 2 = 21.1.Write 15 as a product of primefactors.2.Write 87 as a product of primefactors.3.Write 38 as a product of primefactors.4.Write 109 as a product of primefactors.5.Write 29 as a product of primefactors.6.Write 51 as a product of primefactors.7.Write 105 as a product of primefactors.8.Write 74 as a product of primefactors.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · b068fdcf
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Practice + answer key · 2 pages

Factors & multiples

What you’ll practice

Express an integer greater than 1 as a product of primes.

Keep dividing by prime factors until nothing composite remains. Leave repeated factors in the product so you can multiply them back to check the original number.

How this skill works

Divide by the smallest available prime factor and continue with the remaining quotient. Stop when the quotient becomes 1.

A prime starting number is already its own prime factorization. A composite starting number must be broken down until no composite factor remains.

Worked example

Write 84 as a product of prime factors.
  1. 84 ÷ 2 = 42, then 42 ÷ 2 = 21.
  2. 21 ÷ 3 = 7, and 7 is prime.
  3. Multiply back: 2 × 2 × 3 × 7 = 84.

Answer: 2 × 2 × 3 × 7

Teaching notes

  • Do not stop with a composite factor such as 21.
  • Keep every repeated prime factor in the product.
Practice questions
  1. Write 15 as a product of prime factors.
  2. Write 87 as a product of prime factors.
  3. Write 38 as a product of prime factors.
  4. Write 109 as a product of prime factors.
  5. Write 29 as a product of prime factors.
  6. Write 51 as a product of prime factors.
  7. Write 105 as a product of prime factors.
  8. Write 74 as a product of prime factors.
Answers and steps
  1. 3 × 5
    1. 15 ÷ 3 = 5; record the prime factor 3.
    2. 5 ÷ 5 = 1; record the prime factor 5.
    3. The prime factors multiply back to the original number: 3 × 5 = 15.
  2. 3 × 29
    1. 87 ÷ 3 = 29; record the prime factor 3.
    2. 29 ÷ 29 = 1; record the prime factor 29.
    3. The prime factors multiply back to the original number: 3 × 29 = 87.
  3. 2 × 19
    1. 38 ÷ 2 = 19; record the prime factor 2.
    2. 19 ÷ 19 = 1; record the prime factor 19.
    3. The prime factors multiply back to the original number: 2 × 19 = 38.
  4. 109
    1. 109 ÷ 109 = 1; record the prime factor 109.
    2. The prime factors multiply back to the original number: 109 = 109.
  5. 29
    1. 29 ÷ 29 = 1; record the prime factor 29.
    2. The prime factors multiply back to the original number: 29 = 29.
  6. 3 × 17
    1. 51 ÷ 3 = 17; record the prime factor 3.
    2. 17 ÷ 17 = 1; record the prime factor 17.
    3. The prime factors multiply back to the original number: 3 × 17 = 51.
  7. 3 × 5 × 7
    1. 105 ÷ 3 = 35; record the prime factor 3.
    2. 35 ÷ 5 = 7; record the prime factor 5.
    3. 7 ÷ 7 = 1; record the prime factor 7.
    4. The prime factors multiply back to the original number: 3 × 5 × 7 = 105.
  8. 2 × 37
    1. 74 ÷ 2 = 37; record the prime factor 2.
    2. 37 ÷ 37 = 1; record the prime factor 37.
    3. The prime factors multiply back to the original number: 2 × 37 = 74.