# How can GCF help when simplifying a fraction?

Apr 4, 2016

#### Explanation:

Let a fraction be $\frac{312}{168}$.

Normally, as numerator and denominator are even, we will divide each by $2$ and then again check numerator and denominator and use divisibility rule to examine the number that can divide them further.

This will go on till they cannot be divided any further by a number other than $1$.

On the contrary if we take GCF of $312$ and $168$, we can divide numerator and denominator by GCF and we will get simplified fraction. In above case, GCF is $24$ and dividing by $24$, we get

$\frac{312}{168} = \frac{13 \times 24}{7 \times 24} = \frac{13}{7}$

In earlier method it would have been

$\frac{312}{168} = \frac{2 \times 156}{2 \times 84} = \frac{156}{84} = \frac{2 \times 78}{2 \times 42} = \frac{78}{42}$

= $\frac{2 \times 39}{2 \times 21} = \frac{39}{21} = \frac{3 \times 13}{3 \times 7} = \frac{13}{7}$