Question

What is the least number that must be subtracted from 1056 so the number is divisible by 23?

• A. 18
• B. 21
• C. 22
• D. 19

Answer 1

The correct option is B 21

We express 1056 in terms of 23 using Euclid's division lemma which states that given positive integers $a$ and $b,$ there exist unique pair of integers $b$ and $r$ such that
$a=bq+r.$
Here, we take $a=1056$ and $b=23.$
Also, $1056=23\times 45+21.$
As we can observe, $1056-21$ is divisible by 23.
$\therefore$ On subtracting 21 from 1056, the resultant is divisible by 23.