Question

Find the greatest number that will divide $138,183$ and $243$, learning remainders $3$ in each case.

Answer 1

Let the no. be x.

$138\Rightarrow x\times {\alpha }_1+3.$

$x\times {\alpha }_1=135$

similarly,

$x\times {\alpha }_2+3=183$

$x{\alpha }_2=180.$

similarly

$x{\alpha }_3=243-3$

$=240.$

Taking HCF OF 135, 180 & 240.

$\therefore$ Highest common factor $=5\times 3$

$=15.$

$\therefore$ greatest no which will divide 138,183 &

243 and leaves remainder as '3' = 15