Question

find the gcf for the list.

(147y^3), (98y^2)

the gcf is

Explanation:

🆕 New Concept Discovered: Greatest Common Factor of Monomials
Finding the largest shared factor of numbers and variables.

Step 1: Find the GCF of the numerical coefficients

To find the Greatest Common Factor (GCF) of the coefficients \(147\) and \(98\), we look at their prime factorizations:

$$ 147 = 3 \times 49 = 3 \times 7^2 $$

$$ 98 = 2 \times 49 = 2 \times 7^2 $$

The common prime factor is \(7^2\):

$$ \text{GCF}(147, 98) = 49 $$

Step 2: Find the GCF of the variable parts

For the variable parts \(y^3\) and \(y^2\), we take the variable with the smallest exponent that appears in both terms:

$$ \text{GCF}(y^3, y^2) = y^2 $$

Step 3: Combine the results

Multiply the numerical GCF by the variable GCF:

$$ \text{GCF}(147y^3, 98y^2) = 49y^2 $$

Answer:

\(49y^2\)