Question

Find the greatest number which divides $285$ and $1249$ leaving remainders $9$ and $7$ respectively.

Answer 1

The required number is HCF of 276 and 1242.

$276=2\times 2\times 3\times 23=2^2\times 3^1\times {23}^1$

$1242=2\times 3\times 3\times 3\times 23=2^1\times 3^3\times {23}^1$

HCF of $276$ and $1242=2^1\times 3^1\times {23}^1$

$=138$

The required greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.