Question

Find the greatest number, by which when $472,832$ and $1372$ are divided, the remainders are the same.

Answer 1

$472,832,1372$

$\Rightarrow$ let d divides each number and leaves R.

$\Rightarrow$ $472-r,832-r,1372-r$.

$\Rightarrow (832-r)-(472-r)$ and $(1372-r)-(832-r)$ are divisible by d.

$\Rightarrow 360$ & $540$ are divisible by d

$\Rightarrow$ H.C.F of $360$ & $540$ is $180$.

i.e., $360=180\times 2$

$540=180\times 3$.