Factor Calculator

Pares de Factores

Encuentre los conjuntos de dos números que multiplicados entre sí den como resultado su número objetivo.

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. The total number of factor pairs equals half the total factor count, rounded up (perfect squares have an extra equal pair).

Finding All Factor Pairs

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

Pair Matching Diagram

1
1 × 30 = 30
30
2
2 × 15 = 30
15
3
3 × 10 = 30
10
5
5 × 6 = 30
6
30 has 4 factor pairs

Factor Pairs Worked Examples

30

4 factor pairs

(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 (30 = 6² - 6). The prime factorization 2 × 3 × 5 means 30 has (1+1)(1+1)(1+1) = 8 factors forming 4 pairs.

45

3 factor pairs

72

6 factor pairs

120

8 factor pairs

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 (1, 12), (2, 6), (3, 4). The product of 2 negative numbers is positive. Factor calculators typically list only positive factor pairs because most practical applications (division, fraction simplification, GCF) use positive integers.