GCF of 40a^3 and 32a^2
both 40 and 32 divide by 8
both a^3 and a^2 divide by a^2
The GCF is 8a^2
To find the greatest common factor (GCF) of 40a^3 and 32a^2, let's break down each term into its prime factors:
40a^3 = 2^3 * 5 * a * a * a
32a^2 = 2^5 * a * a
Now, let's identify the common factors and take the lowest exponent for each factor:
The common factors are 2^3, a, and a.
Taking the lowest exponent for each factor, the GCF is:
GCF = 2^3 * a * a = 8a^2
To find the greatest common factor (GCF) of 40a^3 and 32a^2, we need to factorize both terms and identify the common factors.
Step 1: Factorize 40a^3
The prime factorization of 40 is 2 * 2 * 2 * 5 = 2^3 * 5.
Hence, 40a^3 can be written as 2^3 * 5 * a * a * a = 8a^3 * 5.
Step 2: Factorize 32a^2
The prime factorization of 32 is 2 * 2 * 2 * 2 * 2 = 2^5.
Hence, 32a^2 can be written as 2^5 * a^2.
Step 3: Identify the common factors
Now, let's compare the prime factors of 40a^3 and 32a^2 to find the common factors.
The common factors are: 2^3 and a^2.
Step 4: Calculate the GCF
The GCF is the product of the common factors:
GCF(40a^3, 32a^2) = 2^3 * a^2 = 8a^2.
Therefore, the greatest common factor of 40a^3 and 32a^2 is 8a^2.