Question

Find the greatest number which divides $285$ and $1,249$, leaving remainders $9$ and $7$ respectively.

Answer 1

Finding the greatest number which divides $285$ and $1,249$ leaving remainders $9$ and $7$

To find the greatest number, first of all we subtract the respective remainders $9$ and $7$ from the given numbers.

$285-9=276$

$1,249-7=1,242$

Now finding the Prime Factors of $276$ and $1,242$ to find the HCF

Prime Factors of $276$ $=2\times 2\times 3\times 3$

Prime Factors of $1,242$ $=2\times 3\times 3\times 3\times 23$

Common Factors of $276$ and $1,242$ are $2$, $3$, and $23$

Thus, the HCF of $276$ and $1,242$ is $2\times 3\times 23=138$

Hence, the greatest number which divides $285$ and $1,249$, leaving remainders $9$ and $7$ is $138$