Question

Find the greatest number that will divide $95,114$ and $129$ leaving a remainder $5,4$ and $3$ respectively.

Answer 1

Subtracting remainder from the given numbers.

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

$$\begin{gathered} 95-5=90 \\ 114-4=110 \\ 129-3=126 \end{gathered}$$

Finding the H.C.F of $90,110$ and $126$.

Prime factorisation of $90=2\times 3\times 3\times 5$.

Prime factorisation of $110=2\times 5\times 11$.

Prime factorisation of $126=2\times 3\times 3\times 7$.

H.C.F of $90,110$ and $126=2$.

Hence, the answer of this question is $2$.