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Factor pairs

Find all the pairs that multiply to make a number.

Practice + answer key · 2 pages

Worksheet settings8 questions · 2 columns · A4
Number range

Select the numbers whose factor pairs will be listed.

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mathsprig-1
Content ID
77a9e970
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1 page
Factor pairsFactor pairs. Practice. List all positive factor pairs of 94. List all positive factor pairs of 82. List all positive factor pairs of 68. List all positive factor pairs of 30. List all positive factor pairs of 54. List all positive factor pairs of 19. List all positive factor pairs of 12. List all positive factor pairs of 40.Name __________________________Date _______________Factor pairsWrite every positive factor pair for each number.Worked exampleList the positive factor pairs of 36. → 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6Test first factors from 1 through 6, the square root of 36.1.List all positive factor pairs of94.2.List all positive factor pairs of82.3.List all positive factor pairs of68.4.List all positive factor pairs of30.5.List all positive factor pairs of54.6.List all positive factor pairs of19.7.List all positive factor pairs of12.8.List all positive factor pairs of40.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 77a9e970
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Practice + answer key · 2 pages

Factors & multiples

What you’ll practice

List all positive factor pairs without duplicating reversed pairs.

Start with 1 and the number itself, then test the next possible factor. Working in pairs helps you find every factor without listing the same pair twice.

How this skill works

Start with 1 multiplied by the number itself. Test larger possible first factors and keep only exact divisions.

Stop when the first factor would be larger than the second. A square number has one middle pair with equal factors; write that pair once.

Worked example

List the positive factor pairs of 36.
  1. Test first factors from 1 through 6, the square root of 36.
  2. 1, 2, 3, 4 and 6 divide 36 exactly.
  3. Pair each with its quotient; reversed pairs would repeat the same relationship.

Answer: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6

Teaching notes

  • A missing factor pair often means a small divisor was skipped.
  • Check each pair by multiplication.
Practice questions
  1. List all positive factor pairs of 94.
  2. List all positive factor pairs of 82.
  3. List all positive factor pairs of 68.
  4. List all positive factor pairs of 30.
  5. List all positive factor pairs of 54.
  6. List all positive factor pairs of 19.
  7. List all positive factor pairs of 12.
  8. List all positive factor pairs of 40.
Answers and steps
  1. 1 × 94, 2 × 47
    1. Check divisors from 1 through 9; pair each exact divisor with 94 divided by that divisor.
    2. The complete set is 1 × 94, 2 × 47.
  2. 1 × 82, 2 × 41
    1. Check divisors from 1 through 9; pair each exact divisor with 82 divided by that divisor.
    2. The complete set is 1 × 82, 2 × 41.
  3. 1 × 68, 2 × 34, 4 × 17
    1. Check divisors from 1 through 8; pair each exact divisor with 68 divided by that divisor.
    2. The complete set is 1 × 68, 2 × 34, 4 × 17.
  4. 1 × 30, 2 × 15, 3 × 10, 5 × 6
    1. Check divisors from 1 through 5; pair each exact divisor with 30 divided by that divisor.
    2. The complete set is 1 × 30, 2 × 15, 3 × 10, 5 × 6.
  5. 1 × 54, 2 × 27, 3 × 18, 6 × 9
    1. Check divisors from 1 through 7; pair each exact divisor with 54 divided by that divisor.
    2. The complete set is 1 × 54, 2 × 27, 3 × 18, 6 × 9.
  6. 1 × 19
    1. Check divisors from 1 through 4; pair each exact divisor with 19 divided by that divisor.
    2. The complete set is 1 × 19.
  7. 1 × 12, 2 × 6, 3 × 4
    1. Check divisors from 1 through 3; pair each exact divisor with 12 divided by that divisor.
    2. The complete set is 1 × 12, 2 × 6, 3 × 4.
  8. 1 × 40, 2 × 20, 4 × 10, 5 × 8
    1. Check divisors from 1 through 6; pair each exact divisor with 40 divided by that divisor.
    2. The complete set is 1 × 40, 2 × 20, 4 × 10, 5 × 8.