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Greatest common factor

Find the greatest factor shared by two numbers.

Practice + answer key · 2 pages

Worksheet settings8 questions · 2 columns · A4
Number range

Both numbers in each pair are independently chosen inside these bounds.

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mathsprig-1
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3783d79f
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Greatest common factorGreatest common factor. Practice. Find the greatest common factor of 6 and 37. Find the greatest common factor of 20 and 39. Find the greatest common factor of 49 and 36. Find the greatest common factor of 40 and 32. Find the greatest common factor of 44 and 33. Find the greatest common factor of 35 and 25. Find the greatest common factor of 28 and 45. Find the greatest common factor of 48 and 57.Name __________________________Date _______________Greatest common factorFind the greatest common factor of each pair.Worked exampleFind the greatest common factor of 18 and 24. → 6Factors of 18: 1, 2, 3, 6, 9, 18.1.Find the greatest common factorof 6 and 37.2.Find the greatest common factorof 20 and 39.3.Find the greatest common factorof 49 and 36.4.Find the greatest common factorof 40 and 32.5.Find the greatest common factorof 44 and 33.6.Find the greatest common factorof 35 and 25.7.Find the greatest common factorof 28 and 45.8.Find the greatest common factorof 48 and 57.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 3783d79f
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Practice + answer key · 2 pages

Factors & multiples

What you’ll practice

Identify the greatest common positive factor of two positive integers.

List the factors of each number and look for the ones they share. The largest shared factor is the greatest common factor, also called GCF or HCF.

How this skill works

A common factor divides both numbers exactly. List the factor sets or use a repeated-division method to find their shared factors.

Choose the greatest shared factor, not the greatest number in either individual list. Some pairs share only 1.

Worked example

Find the greatest common factor of 18 and 24.
  1. Factors of 18: 1, 2, 3, 6, 9, 18.
  2. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
  3. Their common factors are 1, 2, 3 and 6, so the greatest is 6.

Answer: 6

Teaching notes

  • Check that your answer divides both numbers.
  • A greatest common factor cannot exceed the smaller starting number.
Practice questions
  1. Find the greatest common factor of 6 and 37.
  2. Find the greatest common factor of 20 and 39.
  3. Find the greatest common factor of 49 and 36.
  4. Find the greatest common factor of 40 and 32.
  5. Find the greatest common factor of 44 and 33.
  6. Find the greatest common factor of 35 and 25.
  7. Find the greatest common factor of 28 and 45.
  8. Find the greatest common factor of 48 and 57.
Answers and steps
  1. 1
    1. Factors of 6: 1, 2, 3, 6.
    2. Factors of 37: 1, 37.
    3. Common factors are 1. The greatest is 1.
  2. 1
    1. Factors of 20: 1, 2, 4, 5, 10, 20.
    2. Factors of 39: 1, 3, 13, 39.
    3. Common factors are 1. The greatest is 1.
  3. 1
    1. Factors of 49: 1, 7, 49.
    2. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
    3. Common factors are 1. The greatest is 1.
  4. 8
    1. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
    2. Factors of 32: 1, 2, 4, 8, 16, 32.
    3. Common factors are 1, 2, 4, 8. The greatest is 8.
  5. 11
    1. Factors of 44: 1, 2, 4, 11, 22, 44.
    2. Factors of 33: 1, 3, 11, 33.
    3. Common factors are 1, 11. The greatest is 11.
  6. 5
    1. Factors of 35: 1, 5, 7, 35.
    2. Factors of 25: 1, 5, 25.
    3. Common factors are 1, 5. The greatest is 5.
  7. 1
    1. Factors of 28: 1, 2, 4, 7, 14, 28.
    2. Factors of 45: 1, 3, 5, 9, 15, 45.
    3. Common factors are 1. The greatest is 1.
  8. 3
    1. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
    2. Factors of 57: 1, 3, 19, 57.
    3. Common factors are 1, 3. The greatest is 3.