Find Greatest Common Factor (GCF) of Monomials - Grade 11 Math Questions With Detailed Solutions

How to find the greatest common factor (GCF) of two or more monomials in math? Grade 11 math questions are presented along with Detailed Solutions and explanations are included.

What is the greatest common factor (GCF) of monomials?

The greatest common factor of two or more monomials is the greatest monomial that divides evenly into all these monomials. It is found by first finding the prime factorization Prime Factorization of each monomial.

Example 1: Find greatest common factor of the monomials 12 x and 18 x^{ 2}.

Solution

1) Write the prime factorization of the monomial 12 x : 12 x = 2 × 2 × 3 × x

2) Write the prime factorization of the monomial 18 x^{ 2} : 18 x^{ 2} = 2 × 3 × 3 × x × x

The greatest of the common factor (GCF) of 12 x and 18 x^{ 2} is the product of all common factors in the prime factorization above:

GCF(12 x,18 x^{ 2}) = 2 × 3 × x = 6 x

Example 2: Find greatest common factor of the monomials 30x^{ 2}y^{ 3}, 42x^{ 3}y^{ 2} and 18 x^{ 2}y^{ 2}

Solution

1) Write the prime factorization of the monomial 30x^{ 2}y^{ 3} = 2 × 3 × 5 × x × x × y × y × y

2) Write the prime factorization of the monomial 42x^{ 3}y^{ 2} = 2 × 3 × 7 × x × x × x × y × y

3) Write the prime factorization of the monomial 18 x^{ 2} y^{ 2} = 2 × 3 × 3 × x × x × y × y

The greatest of the common factor (GCF) of 30x^{ 2}y^{ 3}, 42x^{ 3}y^{ 2} and 18 x^{ 2}y^{ 2} is the product of all common factors in the prime factorization above:

GCF(30x^{ 2}y^{ 3}, 42x^{ 3}y^{ 2} and 18 x^{ 2}y^{ 2}) = 2 × 3 × x × x × y × y = 6 x^{ 2} y^{ 2}