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Question
What is the least number that must be subtracted from 1056 so the number is divisible by 23?
What is the least number that must be subtracted from 1056 so the number is divisible by 23?
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Solution
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=23×45+21.
As we can observe, 1056−21 is divisible by 23.
∴ On subtracting 21 from 1056, the resultant is divisible by 23.
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=23×45+21.
As we can observe, 1056−21 is divisible by 23.
∴ On subtracting 21 from 1056, the resultant is divisible by 23.
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