Question

What is `12414/155679` in simplest form?

Answer 1

`12414/155679 = 4138/51893`

Explanation:

One method of finding the greatest common factor (GCF) of two numbers goes as follows:

• Divide the larger number by the smaller to give a quotient and remainder.

• If the remainder is `0` then the smaller number is the GCF.

• Otherwise repeat with the smaller number and the remainder.

In our example, we can find the GCF of `12414` and `155679` as follows:

`155679/12414 = 12" "` with remainder `6711`

`12414/6711 = 1" "` with remainder `5703`

`6711/5703 = 1" "` with remainder `1008`

`5703/1008 = 5" "` with remainder `663`

`1008/663 = 1" "` with remainder `345`

`663/345 = 1" "` with remainder `318`

`345/318 = 1" "` with remainder `27`

`318/27 = 11" "` with remainder `21`

`27/21 = 1" "` with remainder `6`

`21/6 = 3" "` with remainder `3`

`6/3 = 2" "` with remainder `0`

So the GCF is `3`

So:

`12414/155679 = (12414/3)/(155679/3) = 4138/51893`

This is in simplest form.

Answer 2

`12414/155679=4138/51893`

Explanation:

We have: `12414/155679`

To reduce this to simplest form, we can try estimating to find a possible factor of the expression. These numbers are well past any times tables I ever learned.

Right away, we can see that `2` is not a factor since we have even and odd numbers in the numerator and denominator.

But `3` does look promising since the first part of both numbers divide by `3` and maybe the last part as well.

Then: `12414/155679=(12414/3)/(155679/3)=4138/51893`

Can we go farther? We can see that again `2` is not a factor of both since it will not divide evenly into `51893`.

Lets try `3`: `51893/3=17297.67` so we are done.