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:Â Simplify `\frac{16}{40}`
Solution:
STEP 1:Â 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.
So, Highest Common Factor (HCF) of 16 and 40 is 8.
Again, we see Highest Common Factor (HCF) of 16 and 40 is 8.
STEP 2:Â 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:Â Can we simplify?
 `\frac{21}{79}`
Solution:Â 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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