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In order to find the greatest common factor of monomials follow these two steps.

Step 1. Find the prime factorization of each monomial.

Step 2. Take the product of all common factors

Example of finding the GCF of a monomial.

Find the greatest common factor of 
27x^2yq^5 and 15x^3q^3

Step 1. Find the prime factorization of each monomial
27x^2yq^5 = 3 3 3 x x  y  q q q q q
15x^3q^3 =  3  5  x x x  q q q

Step 2. Take the product of common factors
3x^2q^3

How is Least Common Multiple different than Greatest Common Factor?

The least common multiple is the smallest positive integer that is a multiple of two or more integers.

For example the least common multiple of 4 and 16 is 16

The GCF is the greatest integer that divides evenly into two or more of integers.

The GCF of 4 and 16 is 4

Finding the greatest common factor of monomials

Example 2 Finding the Greatest Common Factor (GCF)

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How to find the GCF

Greatest common factor using a factor tree
Finding the GCF can become confusing and frustrating if the only method you use is trial and error. Here is one proven method for finding the GCF.
Steps for finding greatest common factor or GCF picture has lady standing by a dry erase board with steps written down
1. Set up factor tree
2. Factor down to prime numbers I like to circle or underline prime numbers.
3.Multiply common factors 3x5 = 15 is the GCF
Steps for finding greatest common factor or GCF picture has lady standing by a dry erase board with steps written down

Greatest Common Factor Definition

For example, the greatest common factor of 24 and 36 is 12 because it is the largest positive integer that will divide  into both numbers without a remainder.
24/12 = 2     36/12 = 3

Integers are positive or negative whole numbers. Integers do not contain fractions

  • Whole numbers greater than 0 are positive integers
  • Whole numbers less than 0 are negative integers
  • Zero is an integer and is considered "neutral"
The GCF or Greatest Common Factor is simply the largest positive integer that will divide exactly into two or more numbers.