An integer that divides into another integer exactly is called a Factor. In other words, if any integer is divided by another integer without leaving any remainder, then the latter is the factor of the former.

For example, 2 is a factor of 8, because 2 divides evenly into 8.
The quantities that are being multiplied together to get a product are called factors.
For example, 15 × 4 = 60 implies that 15 and 4 are the factors of 60.

More About Factor

The factor of a polynomial P(x) is any polynomial that divides evenly into the polynomial P(x).
For example, y - 1 is a factor of y^{2} - 3y + 2.
Factor tree is the graphical representation of the factors of a number.

Video Examples: Multiples and Factors

Example of Factor

By multiplying (x + 2) and (x + 3), we get x^{2} + 5x + 6. So, (x + 2) and (x + 3) are the factors of x^{2} + 5x + 6.

Solved Example on Factor

Ques: Which of the following shows the factors of 30?

Choices:

A. 30 = 5 × 2 × 2
B. 30 = 5 × 5 × 2
C. 30 = 5 × 3 × 2
D. 30 = 5 × 3 × 3
Correct Answer: C

Solution:

Step 1: The number 30 can be written as 5 × 6.
Step 2: 5 × 6 = 5 × 3 × 2 [Rewrite 6.]
Step 3: So, the factors of 30 are 5, 3, and 2 or 30 = 5 × 3 × 2.