Factors

Key notes:

In mathematics, a factor is a number that divides another number completely without leaving a remainder. Understanding factors is essential for various topics in math, including algebra and number theory.

Here’s a simple breakdown of the concept:

Definition of a Factor:

• A factor of a number is an integer that divides the number evenly.
  • For example, 2 is a factor of 8 because 8 ÷ 2 = 4 with no remainder.

Finding Factors:

• To find factors, you can start by testing numbers from 1 up to the number itself to see which ones divide it evenly.
• Example: To find the factors of 12, test numbers 1, 2, 3, 4, 6, and 12:
  • 12 ÷ 1 = 12 (Factor)
  • 12 ÷ 2 = 6 (Factor)
  • 12 ÷ 3 = 4 (Factor)
  • 12 ÷ 4 = 3 (Factor)
  • 12 ÷ 6 = 2 (Factor)
  • 12 ÷ 12 = 1 (Factor)
• So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Prime Factors:

• Prime factors are factors that are prime numbers. For instance, the prime factors of 12 are 2 and 3, since 12 = 2 × 2 × 3.

Factor Pairs:

• Factor pairs are two numbers that multiply together to give the original number.
  • For 12, the factor pairs are (1, 12), (2, 6), and (3, 4).

Greatest Common Factor (GCF):

• The GCF is the largest factor that two or more numbers share.
  • For example, the GCF of 12 and 18 is 6.

let’s practice!