What is the greatest common factor of 36x^3y^2 and 48x^2y?

What is the greatest common factor of 36x^3y^2 and 48x^2y?

• A. 12xy
• B. 12x^2y
• C. 24x^2y^2
• D. 6xy

Answer: (A)

To find the greatest common factor (GCF) of the expressions \( 36x^3y^2 \) and \( 48x^2y \), it's essential to consider both the numerical coefficients and the variables separately. First, let's break down the coefficients. - The number 36 can be factored into primes as \( 36 = 2^2 \times 3^2 \). - The number 48 can be factored into primes as \( 48 = 2^4 \times 3^1 \). Next, to find the GCF of the coefficients, we take the minimum exponent for each prime factor: - For the factor of 2, the minimum between \( 2^2 \) (from 36) and \( 2^4 \) (from 48) is \( 2^2 \). - For the factor of 3, the minimum between \( 3^2 \) (from 36) and \( 3^1 \) (from 48) is \( 3^1 \). Combining these gives us the GCF of the numbers: \( 2^2 \times 3^1 = 4 \times

To find the greatest common factor (GCF) of the expressions ( 36x^3y^2 ) and ( 48x^2y ), it's essential to consider both the numerical coefficients and the variables separately.

First, let's break down the coefficients.

• The number 36 can be factored into primes as ( 36 = 2^2 \times 3^2 ).

• The number 48 can be factored into primes as ( 48 = 2^4 \times 3^1 ).

Next, to find the GCF of the coefficients, we take the minimum exponent for each prime factor:

• For the factor of 2, the minimum between ( 2^2 ) (from 36) and ( 2^4 ) (from 48) is ( 2^2 ).

• For the factor of 3, the minimum between ( 3^2 ) (from 36) and ( 3^1 ) (from 48) is ( 3^1 ).

Combining these gives us the GCF of the numbers:

( 2^2 \times 3^1 = 4 \times