# What is 12414/155679 in simplest form?

Mar 28, 2017

$\frac{12414}{155679} = \frac{4138}{51893}$

#### 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:

$\frac{155679}{12414} = 12 \text{ }$ with remainder $6711$

$\frac{12414}{6711} = 1 \text{ }$ with remainder $5703$

$\frac{6711}{5703} = 1 \text{ }$ with remainder $1008$

$\frac{5703}{1008} = 5 \text{ }$ with remainder $663$

$\frac{1008}{663} = 1 \text{ }$ with remainder $345$

$\frac{663}{345} = 1 \text{ }$ with remainder $318$

$\frac{345}{318} = 1 \text{ }$ with remainder $27$

$\frac{318}{27} = 11 \text{ }$ with remainder $21$

$\frac{27}{21} = 1 \text{ }$ with remainder $6$

$\frac{21}{6} = 3 \text{ }$ with remainder $3$

$\frac{6}{3} = 2 \text{ }$ with remainder $0$

So the GCF is $3$

So:

$\frac{12414}{155679} = \frac{\frac{12414}{3}}{\frac{155679}{3}} = \frac{4138}{51893}$

This is in simplest form.

Apr 14, 2017

$\frac{12414}{155679} = \frac{4138}{51893}$

#### Explanation:

We have: $\frac{12414}{155679}$

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: $\frac{12414}{155679} = \frac{\frac{12414}{3}}{\frac{155679}{3}} = \frac{4138}{51893}$

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 $3$: $\frac{51893}{3} = 17297.67$ so we are done.