Factor Calculator

Factor Pairs

Calculate and display all factor pairs that multiply to your target integer.

What are Factor Pairs?

A factor pair is a set of 2 whole numbers that multiply together to produce a given number. The number 30 has 4 factor pairs: (1, 30), (2, 15), (3, 10), and (5, 6). Every factor pair represents a way to express the number as a product of exactly 2 integers. A factor pair calculator lists all such pairs instantly.

Factor pairs connect directly to rectangular arrays in geometry — each pair defines a rectangle with the given area. They are the foundation for factoring algebraic expressions and understanding multiplication relationships.

Finding All Factor Pairs

Select a number to see its factor pairs displayed as connected matching blocks.

Pair Matching Diagram

1
×
30
2
×
15
3
×
10
5
×
6

Examples of Factor Pairs

Expand each card below to see a detailed factor analysis.

30(1,30), (2,15), (3,10), (5,6)

30 has 4 factor pairs. Each pair multiplies to 30. The pair (5, 6) contains consecutive integers, a property unique to numbers one less than a perfect square.

45(1,45), (3,15), (5,9)
72(1,72), (2,36), (3,24), (4,18), (6,12), (8,9)

Frequently Asked Questions

Yes, in formal number theory, factors can be negative. The factor pairs of 12 include (-1, -12), (-2, -6), (-3, -4) as well as positive ones. Most basic arithmetic lists only positive factor pairs.