To find the greatest common factor (GCF) of the terms 14xy^2 and 70y^3, we need to determine the highest power of each prime factor that appears in both terms.
Let's break down the terms:
14xy^2 can be written as 2 * 7 * x * y * y
70y^3 can be written as 2 * 5 * 7 * y * y * y
From these breakdowns, we can see that the shared prime factors are 2, 7, and y^2.
Taking the highest power of each common prime factor:
The highest power of 2 that appears in both terms is 2 (2^1 in 14xy^2 and 2^1 in 70y^3).
The highest power of 7 that appears in both terms is 1 (7^1 in 14xy^2 and 7^1 in 70y^3).
The highest power of y that appears in both terms is 2 (y^2 in 14xy^2 and y^2 in 70y^3).
Therefore, the GCF of the terms 14xy^2 and 70y^3 is 2 * 7 * y^2, which can be written as 14y^2.
Find the GCF (greatest common factor) of the following terms.
{14xy^2,70y^3}
1 answer
1 answer