Question

Find the greatest number which exactly divides $81,117$

Answer 1

To find the greatest number which exactly divides $81,117$, we need to find the $HCF$ of both the numbers.( we can use any method, Prime Factorisation Method or Continued Division Method)

Here we are using Continued Division Method

In Continued Division Method we divide the larger number by the smaller number. In the next step we divide the divisor of the first step with the remainder in the first step, and repeat the process until we get $0$ in the remainder. The divisor in the step where we get remainder as $0$ is the HCF.

Step 1: leave the smallest number first and find the HCF of $81,117$

$$\begin{gathered} 81\overline{)117}\overline{)1} \\ \underline{-81} \\ 36\overline{)81}\overline{)2} \\ \underline{-72} \\ 9\overline{)36}\overline{)4} \\ \underline{-36} \\ 0 \end{gathered}$$

here $9$ is the divisor in the last step where the remainder is $0$, hence $HCF=9$