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How do you find factor pairs?

Published in Number Factors 2 mins read

Factor pairs are found by identifying two numbers that, when multiplied together, equal a specific target number. As the reference states, when a number is divided by one factor, the answer is another factor. These two numbers form a factor pair. For example, if 3 and 4 are multiplied together to make 12, then 3 and 4 are considered a factor pair of 12.

Here's a step-by-step process to find factor pairs:

  1. Start with 1: Begin by dividing the target number by 1. The result will always be the target number itself. This gives you your first factor pair. For instance, the first pair for 12 is 1 and 12 (1 x 12 = 12).

  2. Check for Divisibility by 2: See if the target number is divisible by 2 (if it is an even number). If it is, the result of the division will be its paired factor. For example, for 12, 12 ÷ 2 = 6, so 2 and 6 form a pair.

  3. Continue Checking Higher Numbers: Progress sequentially, checking for divisibility by 3, 4, and so on. If the division results in a whole number (no remainders), you have found another pair.

    • For 12:
      • 12 ÷ 3 = 4, therefore, 3 and 4 are a pair.
      • If you checked 4, you'd get 12 ÷ 4 = 3 (already found)

  4. Stop When Factors Repeat: Stop checking for divisors when the second factor of a pair is equal to or smaller than the first factor you already found. This signifies that you've found all factor pairs.

Example: Finding Factor Pairs for 24

Let's find the factor pairs for 24 using the steps described above.

Factor Division Calculation Paired Factor
1 24 ÷ 1 = 24 24
2 24 ÷ 2 = 12 12
3 24 ÷ 3 = 8 8
4 24 ÷ 4 = 6 6

The factor pairs for 24 are:

  • 1 and 24
  • 2 and 12
  • 3 and 8
  • 4 and 6

Example: Finding Factor Pairs for 36

Factor Division Calculation Paired Factor
1 36 ÷ 1 = 36 36
2 36 ÷ 2 = 18 18
3 36 ÷ 3 = 12 12
4 36 ÷ 4 = 9 9
6 36 ÷ 6 = 6 6

The factor pairs for 36 are:

  • 1 and 36
  • 2 and 18
  • 3 and 12
  • 4 and 9
  • 6 and 6

Key Takeaways

  • Factor pairs are two numbers that multiply to give a specific product.
  • You find them by systematically dividing a number by smaller numbers.
  • The process is complete when you start repeating factors.
  • Knowing factor pairs is useful for simplifying fractions, solving equations, and more.

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