Question

What are the prime factors of 196?

Answer 1

`196=2^2xx7^2`

Explanation:

`color(green)2` is the SMALLEST prime number that can divide 196 so we'll start with that :

`196/color(blue)2=98`

98 also can be divided by `color(green)2`, so :

`98/color(blue)2 = 49`

`color(green)2` is no longer a divisor of 49, so we must find the next SMALLEST prime number that can divide 49, which is `color(red)7`

`49/color(blue)7=7`

Again, `color(red)7` is a divisor of itself so :

`7/color(blue)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 `color(green)2` and `color(red)7` :

`196=color(blue)(2xx2xx7xx7)=color(blue)2^2xxcolor(blue)7^2`