Question

Find the greatest number that will divide $132,242$ and $382$ leaving a remainder $2$ in each case.

Answer 1

Subtracting remainder from the given numbers.

Firstly, we have to subtract the remainder $2$ from each number, so that each number is exactly divisible by the greatest number.

$$\begin{gathered} 132-2=130 \\ 242-2=240 \\ 382-2=380 \end{gathered}$$

Finding the H.C.F of $130,240$ and $380$.

Prime factorisation of $130=2\times 5\times 13$.

Prime factorisation of $240=2\times 2\times 2\times 2\times 3\times 5$.

Prime factorisation of $380=2\times 2\times 5\times 19$.

H.C.F of $130,240$ and $380=2\times 5=10$.

Hence, the answer of this question is $10$.