Applied Math: Factoring

Factors and Greatest Common Factor
Factors are numbers that are multiplied together to obtain a product. For example, in the equation , the numbers 2 and 3 are factors.

A prime number has only two factors (1 and itself), but other numbers can have many factors.
A common factor is a number that divides exactly into two or more other numbers. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 15 are 1, 3, 5, and 15. The common factors of 12 and 15 are 1 and 3.
A prime factor is also a prime number. Therefore, the prime factors of 12 are 2 and 3. For 15, the prime factors are 3 and 5.

The greatest common factor
(GCF) is the largest number that is a factor of two or more numbers. For example, the factors of 15 are 1, 3, 5, and 15; the factors of 35 are 1, 5, 7, and 35. Therefore, the greatest common factor of 15 and 35 is 5.

Multiples and Least Common Multiple
Often listed out in multiplication tables, multiples are integer increments of a given factor. In other words, dividing a multiple by the factor number will result in an integer.

For example, the multiples of 7 include: .

Dividing 7, 14, 21, 28, or 35 by 7 will result in the integers 1, 2, 3, 4, and 5, respectively.

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers.

For example, the multiples of 3 include 3, 6, 9, 12, 15, etc.; the multiples of 5 include 5, 10, 15, 20, 25, etc.