Question

Find the largest number which divides $509$ and $985$leaving remainder $5$ in each case.

Answer 1

We will take away $5$ from each of the number :

$509$-$5$= $504$

$985$-$5$ = $980$

We will now find the HCF of $504$ and $980$

$504$= $2\times 2\times 2\times 3\times 3\times 7$

$980$=$2\times 2\times 5\times 7\times 7$

HCF= $2\times 2\times 7$=$28$

Hence the largest number that divides both $509$ and $980$ and leaves a remainder $5$ is $28$