Q 60E - Intermediate Algebra

Question

What is the GCF of $y^4,y^5$and$y^{10}$? Write a general rule that tells you how to find the GCF of $y^a,y^b$and$y^c$.

Step-by-Step Solution

Answer

The GCF of $y^4,y^5$and$y^{10}$ is, $y^4$.

The general rule to find the GCF of $y^a,y^b$and $y^c$ are,

• Factor each coefficient into primes. Write all variables with exponents in expanded form.
• List all factors—matching common factors in a column. In each column, circle the common factors.
• Bring down the common factors that all expressions share.
• Multiply the factors.

Step 1 Given terms are,

$y^4,y^5,y^{10}$.

The objective is, we need to find the GCF for the given terms and also need to write the general rule to find GCF for the three terms.

Step 2 First write the given terms in the expanded form.

$$\begin{gathered} y^4=y\times y\times y\times y \\ {y}^5=y\times y\times y\times y\times y \\ {y}^{10}=y\times y\times y\times y\times y\times y\times y\times y\times y\times y \end{gathered}$$

The GCF is,$y^4$.

Step 3 General rule to find the GCF for the three terms.

• Factor each coefficient into primes. Write all variables with exponents in expanded form.
• List all factors—matching common factors in a column. In each column, circle the common factors.
• Bring down the common factors that all expressions share.
• Multiply the factors.