Question

find the largest number that divides 2053 and 967 and leaves a remainder of 5 and 7 respectively

Answer 1

Hi dear

$clearly \: we \: must \: find \: the \: greatest \: number \: which \: divides \:$
(2053-5)=2048
(967-7)=960

So the required number= HCF of 2048 and 960.

Factors of 2048=
$2 ^{11}$
Factors of 960 =
$2 ^{6} \times 3 \times 5$

Common =
$2 ^{6}$
HCF = 64

So,the required number = 64