# Factor

Factors are any of the numbers multiplied to form a product.

Example

In the multiplication sentence 4 × 3 = 12, 4 and 3 are factors and 12 is the product. Both 4 and 3 divide 12. That is, 12 ÷ 4 = 3 with 0 remaining, and 12 ÷ 3 = 4 with 0 remaining.

### factors of a number

The factors of a number are all the numbers that divide that number.

Example

The whole number factors of 12 are 1, 2, 3, 4, 6, and 12.

### factoring

Factoring is the process of writing a number or expression as the product of its factors.

### factor pair

A factor pair is a set of two numbers, that when multiplied, will result in a given product.

Example

In 2 × 6 = 12, the factor pair for 12 is (2, 6). Other factor pairs for 12 include (1, 12) and (3, 4).

### factor tree

A factor tree is a diagram showing factors of a number. The diagram is complete when the prime factors of that number have been found. Different factor trees may be used for the same number, but the prime factorization is the same.

### prime factor

A prime factor is a prime number that is a factor of a whole number.

Example

The factors of 12 are 1, 2, 3, 4, and 6. Of these factors, 2 and 3 are prime factors.

### proper factor

The proper factors of a number are all its factors except the number itself.

Example

The proper factors of 20 are 1, 2, 3, 4, 5, and 10.

See also common factor, greatest common factor, prime factorization, prime numbers.