A dictionary definition is "one of two or more numbers, algebraic expressions, or the like, that when multiplied together produce a given product." That is the definition of the noun. Factor can also be a verb, in which case it means "resolve into factors."

For example, we can factor the expression 2x^2 + 10x - 12 as 2(x+6)(x-1).

Sometimes the word "factor" is used interchangeably with the word "divisor". Though it can be listed among the divisors, we usually do not show "1" as a factor of a number or expression. Generally, a factor is considered to be different from 1 or the whole.

For example,

The factors of 26 are 2 and 13.

The divisors of 26 are 1, 2, 13, and 26.

For example, we can factor the expression 2x^2 + 10x - 12 as 2(x+6)(x-1).

Sometimes the word "factor" is used interchangeably with the word "divisor". Though it can be listed among the divisors, we usually do not show "1" as a factor of a number or expression. Generally, a factor is considered to be different from 1 or the whole.

For example,

The factors of 26 are 2 and 13.

The divisors of 26 are 1, 2, 13, and 26.