How to Simplify a fraction by Highest Common Factor (HCF)

We can very easily simplify a fraction with the help of Highest Common Factor (HCF).

Let’s do an example to understand this concept.

Example: Simplify $\frac{16}{40}$

Solution:

STEP 1: Find the Highest Common Factor(HCF) of 16 and 40

Factors of 16 are:

1, 2, 4, 8, 16

Factors of 40 are:

1, 2, 4, 5, 8, 10, 20, 40

Common factors of 16 and 40 are:

1, 2, 4, 8

Highest Common Factor (HCF) of 16 and 40 is 8.

$Explained with example how a fraction can be simplified by Highest Common Factor(HCF) of numerator and denominator.$

So, Highest Common Factor (HCF) of 16 and 40 is 8.

$Explained with example how a fraction can be simplified by Highest Common Factor(HCF) of numerator and denominator.$

Multiply all left column numbers

2 × 2 × 2 = 8

Again, we see Highest Common Factor (HCF) of 16 and 40 is 8.

STEP 2: Divide the numerator and denominator by their HCF.

The number at the top of a fraction is called the numerator, and the number at the bottom of a fraction is called the denominator.

In $\frac{16}{40}$

16 is numerator and 40 is denominator.

Highest Common Factor of 16 and 40 is 8. So,

$\frac{16\div8}{40\div8}=\frac25$

Thus, simplified form of fraction $\frac{16}{40}$ is $\frac{2}{5}$

Example: Can we simplify?

$\frac{21}{79}$

Solution: Since the only factor common in 21 and 79 is 1. So, Highest Common Factor (HCF) of 21 and 79 is 1.

Thus, the fraction $\frac{21}{79}$ cannot be simplified further.

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