Question

How do you find the prime factorization of 196?

Answer 1

`196=2xx2xx7xx7`

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=4xx49`

but factors of `4` are `2xx2` and that of `49` are `7xx7`. Further `2's` and `7's` are prime numbers and cannot be factorized.

Hence prime factors of `196` are

`196=2xx2xx7xx7`

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.

Answer 2

`196 = 2xx2xx7xx7`

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 = (2xx7)^2`

`= 2xx2xx7xx7`

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

`196` is even `:. div2`

`2|ul(196)`
`2|ul(98)" "larrdiv 2` (even)
`7|ul49`
`7|ul7`
`" "ul1`

`196 = 2xx2xx7xx7`