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factor pair — Definition, Formula & Examples

A factor pair is two whole numbers that you multiply together to get a specific product. For example, 3 and 4 are a factor pair of 12 because 3×4=123 \times 4 = 12.

For a positive integer nn, a factor pair is an ordered or unordered pair of positive integers (a,b)(a, b) such that a×b=na \times b = n. Every factor of nn belongs to at least one such pair.

How It Works

To find all factor pairs of a number, start with 1 and the number itself — that is always the first pair. Then try 2: if the number divides evenly by 2, write down 2 and the quotient as a pair. Continue with 3, 4, 5, and so on. Stop when the smaller number in a pair meets or passes the larger number, meaning you have found all unique pairs.

Worked Example

Problem: Find all the factor pairs of 24.
Start with 1: 1 times 24 equals 24, so (1, 24) is a factor pair.
1×24=241 \times 24 = 24
Try 2: 2 times 12 equals 24, so (2, 12) is a factor pair.
2×12=242 \times 12 = 24
Try 3: 3 times 8 equals 24, so (3, 8) is a factor pair.
3×8=243 \times 8 = 24
Try 4: 4 times 6 equals 24, so (4, 6) is a factor pair.
4×6=244 \times 6 = 24
Check 5: 24 divided by 5 is 4.8, which is not a whole number, so 5 is not a factor. The next candidate, 6, already appeared in the pair (4, 6), so you are done.
Answer: The factor pairs of 24 are (1, 24), (2, 12), (3, 8), and (4, 6).

Why It Matters

Listing factor pairs is a standard skill in grade 4 math (CCSS 4.OA.4) and builds the foundation for finding the greatest common factor, simplifying fractions, and understanding prime factorization in later grades.

Common Mistakes

Mistake: Forgetting that 1 and the number itself form a factor pair.
Correction: Every positive integer nn has the factor pair (1,n)(1, n). Always start your list there so you do not miss it.

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