Question

In the following exercises, find the greatest common factor.

$450,420$

Short answer

The greatest common factor is$30$.

Step-by-step solution

Step 1. Given information

Numbers$450,420$

Step 2. Find Prime factorization

$$\begin{gathered} 450=2\times 3\times 3\times 5\times 5 \\ 420=2\times 2\times 3\times 5\times 7 \end{gathered}$$

Step 3. Find common terms and multiply them 

Multiplying all the prime factors common to both numbers:

$2\times 3\times 5=30$

Therefore, GCF is$30$.