Definition
Factor pair
A factor pair is two positive whole numbers that multiply to make a given whole number.
What it means
Think of making a rectangle from a fixed number of square tiles. Any two side lengths that use every tile form a factor pair. For 24 tiles, a 3-by-8 rectangle gives the pair 3 and 8. List pairs from the outside in and stop when the order would begin to repeat.
Remember it
One product, two partners: multiply the partners and the target number appears.
Example
Find all positive factor pairs of 36. Test possible first factors in order: 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. After 6 × 6, reversing the factors would only repeat pairs, so the list is complete.
Watch for
This elementary sense uses positive whole-number factors. The numbers 3 and 7 are not a factor pair of 24 because 3 × 7 is 21, not 24.
Common mix-up
A factor is one number. A factor pair names the two factors together for one product.
Exact meaning
For a positive whole number, a factor pair is an unordered pair of positive whole-number factors whose product is that number. Swapping the two factors does not create a new pair.