Question

Find the greatest common factor (GCF) of 36q^5, 33q, and 9q^3.

a) 3q
b) q
c) 9q
d) 1

Answer 1

The GCF of 36q^5, 33q, and 9q^3 is 3q.

Step-by-step explanation:

To find the greatest common factor (GCF) of 36q^5, 33q, and 9q^3, we need to determine the largest factor that all three terms have in common. Here's the step-by-step process:

1. Find the prime factorization of each term:
   • 36q^5 = (2^2)(3^2)(q^5)
   • 33q = (3)(11)(q)
   • 9q^3 = (3^2)(q^3)
2. Identify the common factors. In this case, the common factors are 3 and q.
3. Determine the smallest exponent for each common factor. The smallest exponent for 3 is 1, and the smallest exponent for q is 1.
4. So, the GCF of 36q^5, 33q, and 9q^3 is 3q.