Question

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

• A. $64$
• B. $35$
• C. $96$
• D. $72$

Answer 1

The correct option is A $64$

$2053-5=2048$
$967-7=960$

Prime factors of $2048=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Prime factors of $960=2\times 2\times 2\times 2\times 2\times 2\times 3\times 5$
HCF of $2048$ and $960=2\times 2\times 2\times 2\times 2\times 2=64$
Ans-Option A