Factors of a number are the numbers that are multiplied to each other to create that larger number.

Factors include:

• Prime numbers
  Prime numbers are numbers that can only be divided by themselves and 1. They are numbers that can not be created by multiplying any other numbers together.
  eg. 2, 3, 5, 7, 11, 13, 17, 19, etc.
• Composite numbers
  Composite numbers are all the numbers that are not prime numbers.
• Prime factors
  Prime factors are all the prime numbers that are required to multiple together to get any composite number. Most people use a factor tree to find these but it is a very confusing method. Instead simply use a down-step method. Always start by dividing with the smallest prime number and work your way up, using all of the prime numbers smaller than the number if you need to. Avoid using the tree method, it is cumbersome and confusing.
  eg. (for each step, always start by dividing by the smallest prime number)
  What are the prime factors of 56?
  • divide 56 by 2..................2 |56
  • divide 28 by 2..................2 |28
  • divide 14 by 2..................2 |14
  • divide 7 by 7....................7 |7
  • divide 1 by 1....................1 |1
  • so the prime factors are 2, 2, 2, 7 (some teachers also count 1, some don't)
• Greatest common factor
  Greatest = largest number
  Common = the number they have in common
  Factor = multiple
  eg. 24 and 18
  • 24 can be divided by 1, 2, 3, 4, 6, 8, 12
  • 18 can be divided by 1, 2, 3, 6, 9
  • The biggest (or greatest) factor they have in common is 6.

See our Teaching Resources for Math for factoring worksheets, lesson plans, etc.

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