# How do you find the prime factorization of 196?

Mar 13, 2018

$196 = 2 \times 2 \times 7 \times 7$

#### Explanation:

As the last two digits in $196$ are divisible by $4$, $196$ too is divisible by $4$.

Dividing by $4$ we get $49$ and hence

$196 = 4 \times 49$

but factors of $4$ are $2 \times 2$ and that of $49$ are $7 \times 7$. Further $2 ' s$ and $7 ' s$ are prime numbers and cannot be factorized.

Hence prime factors of $196$ are

$196 = 2 \times 2 \times 7 \times 7$

Note : This method of factorization, in which we first find identifiable factors and then proceed until all prime factors are known is called tree method. This is graphically described below. Mar 13, 2018

$196 = 2 \times 2 \times 7 \times 7$

#### Explanation:

It is really useful to know the square numbers up to $400$.

You would then recognise $196$ as ${14}^{2}$ and from there it is easy.

$196 = {14}^{2} = {\left(2 \times 7\right)}^{2}$

$= 2 \times 2 \times 7 \times 7$

If you do not know the square numbers, you have to work it out by dividing by the prime factors.

$196$ is even $\therefore \div 2$

$2 | \underline{196}$
$2 | \underline{98} \text{ } \leftarrow \div 2$ (even)
$7 | \underline{49}$
$7 | \underline{7}$
$\text{ } \underline{1}$

$196 = 2 \times 2 \times 7 \times 7$