How do you find the GCF of #36a^3b, 56ab#?

Question

Zoe Adams · Accepted Answer

GCF of #36a^3b# and #56ab = 4ab# Factors of: #36a^3b = 2×2×3×3×a×a×a×b# #56ab = 2×2×2×7×a×b# If we observe the factors of both, we will find that both have #2, 2, a and b# as common factors in both. Therefore, GCF of #36a^3b# and #56ab = 2×2×a×b = 4ab#.

Everly Taylor · Answer

undefined To find the greatest common factor (GCF) of 36a^3b and 56ab, you can use the method of prime factorization. First, break down each term into its prime factors. Then, identify the common factors and take the smallest exponent for each common factor.

36a^3b can be broken down into prime factors as 2^2 * 3^2 * a^3 * b.
56ab can be broken down into prime factors as 2^3 * 7 * a * b.

Now, identify the common factors:
- Both terms have 2 and a common.
- The smallest exponent for 2 is 2.
- The smallest exponent for a is 1.
- Both terms have b in common.

Therefore, the GCF of 36a^3b and 56ab is 2^2 * a * b, which simplifies to 4ab.