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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)
How to find the GCF
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.
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
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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.