Question

Find the greatest common factor of 36x⁶ and 30x.

a) (6x²)

b) (3x³)

c) (9x⁴)

d) (15x⁵)

Answer 1

To find the greatest common factor (GCF) of 36x⁶ and 30x, factorize both expressions and find the common factors with the lowest exponents.

Step-by-step explanation:

To find the greatest common factor (GCF) of 36x⁶ and 30x, we need to factorize both expressions. GCF can be found by taking the product of the common factors with the lowest exponents.

Factorizing 36x⁶ gives us 2² × 3² × (x)⁶. Factorizing 30x gives us 2 × 3 × (x).

Now, we can find the common factors and their lowest exponents, which gives us 2 × 3 × (x)ⁱ = 6x. Therefore, the greatest common factor of 36x⁶ and 30x is (6x), which is option a).