Question

find the greatest number which divides 279 and 435 leaving the reminder 7 and 10 respectively

Answer 1

Hi,
Here is the answer to your query:-

Numbers given = 279 and 435
Remainder = 7 and 10
New numbers = 279-7 and 435-10
= 272 and 425
Greatest number = HCF(272 and 425)
By Division Lemma
a=bq+r
425=272×1+153
272=153×1+119
153=119×1+34
119=34×3+17
34=17×2+0
HCF = 17
Therefore, greatest number which divides 279 amd 435 leaving remainder 7 and 10 is $\bold{17}$.

$\texttt{THANKS}$