Question

Find the largest number which divides $615$ and $963$ leaving remainder $6$ in each case.

Answer 1

we have to find the largest number which divide $615$ and $963$ leaving remainder $6$ in each case.

so let us subtract $6$ from $615$ and $963$

$\Rightarrow$ $615-6=609$

$\Rightarrow$ $963-6=957$

now lets find the $HCF$

$\Rightarrow$ prime factorisation of $609=29\times 3\times 3$

prime factorisation of $957=29\times 3\times 11$

now lets take out the common factors from both the cases

$\Rightarrow$ $29$ and $3$

$x=29\times 3=87$

∴ $87$ is the number which will divide $615$ and $963$ leaving remainder $6$ in each case.