How to simplify a fraction by using 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}=\frac{2}{5}`

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.


RELATED POST:

How to find ALL Factors of a Number

Prime Factors and Prime Factorization

QUIZ with answers on Factors and Prime Factors of a Number

Common Factors of Numbers

Highest Common Factors (HCF) of Numbers

QUIZ with Answers on Common Factors and Highest Common Factors (HCF) of Numbers

Abundant Number, Deficient Number and Perfect Number