Question

What is the simplest form of $\frac{105}{21}$?

Answer 1

Finding the simplest form of fraction

Simplest form: A fraction is in its simplest form when the numerator and denominator of the fraction are whole numbers that are coprime to each other.

Given fraction is $\frac{105}{21}$

To find the simplest form, we have to find the HCF of the numerator and the denominator of the fraction.

$$\begin{gathered} 105=3\times 5\times 7 \\ 21=3\times 7 \end{gathered}$$

Choose the common factor with the lowest exponent.

HCF$\left(105,21\right)=3\times 7$

HCF$\left(105,21\right)=21$

Now, dividing the numerator and denominator by the HCF to get the simplest form of fraction,

$\begin{array}{rcl}\frac{105}{21}& =& \frac{105÷21}{21÷21}\\ & =& \frac{5}{1}\\ & =& 5\end{array}$

Therefore, the simplest form of $\frac{105}{21}$ is $5$.