Question 21
The greatest number that leaves the same remainder when it divides 30,53 and 99 is
Correct Answer: 23
Solution
If a number leaves the same remainder on dividing 30, 53 and 99, it must divide each of the differences $$53 - 30 = 23$$, $$99 - 53 = 46$$ and $$99 - 30 = 69$$. The greatest such number is their HCF, which is 23.
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