Q. 7 QC - Algebra 1

Question

Find the GCF of each pair of monomials.

$\mathbf{15}\mathit{c}{\mathit{d}}^2\mathbf{,}\mathbf{25}{\mathit{c}}^2\mathit{d}$

Step-by-Step Solution

Answer

The GCF of the given pair of monomials is $\mathbf{5}\mathit{c}\mathit{d}$.

Step 1. Define greatest common factor.

Greatest common factor is the product of common prime factors of two or more whole numbers. It is a greatest number that is factor of both numbers.

Step 2. Factor each number.

Factor each number and write all powers of variables as products.

$\begin{array}{c}15c{d}^2=3\cdot 5\cdot c\cdot d\cdot d\\ 25c^{2}d=5\cdot 5\cdot c\cdot c\cdot d\end{array}$

Step 3. Find the greatest common factor.

Combine common prime factors to find greatest common factor.

$5\cdot c\cdot d=5cd$

Therefore, the GCF of the given pair of monomials is $5cd$.