# What are the prime factors of 196?

Dec 1, 2016

$196 = {2}^{2} \times {7}^{2}$

#### Explanation:

$\textcolor{g r e e n}{2}$ is the SMALLEST prime number that can divide 196 so we'll start with that :

$\frac{196}{\textcolor{b l u e}{2}} = 98$

98 also can be divided by $\textcolor{g r e e n}{2}$, so :

$\frac{98}{\textcolor{b l u e}{2}} = 49$

$\textcolor{g r e e n}{2}$ is no longer a divisor of 49, so we must find the next SMALLEST prime number that can divide 49, which is $\textcolor{red}{7}$

$\frac{49}{\textcolor{b l u e}{7}} = 7$

Again, $\textcolor{red}{7}$ is a divisor of itself so :

$\frac{7}{\textcolor{b l u e}{7}} = 1$

We end the division when we find 1, and the prime factorization of the number 196 is the product of the prime factors in the denominators which are in this case $\textcolor{g r e e n}{2}$ and $\textcolor{red}{7}$ :

$196 = \textcolor{b l u e}{2 \times 2 \times 7 \times 7} = {\textcolor{b l u e}{2}}^{2} \times {\textcolor{b l u e}{7}}^{2}$