Question

Find the greatest common factor of the following monomials.
a) 9x
3y
4
, 15x
2y
2
and 18 xyz

Answer 1

Step-by-step explanation:

The process is similar when you are asked to find the greatest common factor of two or more monomials.

Simply write the complete factorization of each monomial and find the common factors. The product of all the common factors will be the GCF.

For example, let's find the greatest common factor of 10x^310x

3

10, x, cubed and 4x4x4, x:

10x^3=\blueD{2}\cdot 5\cdot \goldD{x}\cdot x\cdot x10x

3

=2⋅5⋅x⋅x⋅x10, x, cubed, equals, start color #11accd, 2, end color #11accd, dot, 5, dot, start color #e07d10, x, end color #e07d10, dot, x, dot, x

4x=\blueD{2}\cdot 2\cdot \goldD{x}4x=2⋅2⋅x4, x, equals, start color #11accd, 2, end color #11accd, dot, 2, dot, start color #e07d10, x, end color #e07d10

Notice that 10x^310x

3

10, x, cubed and 4x4x4, x have one factor of \blueD{2}2start color #11accd, 2, end color #11accd and one factor of \goldD{x}xstart color #e07d10, x, end color #e07d10 in common. Therefore, their greatest common factor is \blueD2\cdot \goldD{x}2⋅xstart color #11accd, 2, end color #11accd, dot, start color #e07d10, x, end color #e07d10 or 2x2x2, x.