# How can GCF help when simplifying a fraction?

How can GCF help when simplifying a fraction?
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Step 1
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
$\frac{312}{168}=\frac{13×24}{7×24}=\frac{13}{7}$
In earlier method it would have been
$\frac{312}{168}=\frac{2×156}{2×84}=\frac{156}{84}=\frac{2×78}{2×42}=\frac{78}{42}$
$\frac{2×39}{2×21}=\frac{39}{21}=\frac{3×13}{3×7}=\frac{13}{7}$