A number consist of two digits whose product is 8 . If the digits are interchanged, the resulting number will exceed the original one by 18 . Find the number.

Question
Factors and multiples
asked 2021-03-05
A number consist of two digits whose product is 8 . If the digits are interchanged, the resulting number will exceed the original one by 18 . Find the number.

Answers (1)

2021-03-06
In this case, there are few enough factors of 8 that we really don't need to come up with anything clever: let's just start trying stuff and see what happens.
1 and 8 are factors of 8. So we could arrange them as 18 and 81. But those are not 18 apart.
2 and 4 are the only other factors of 8. 24 and 42 are 18 apart (and by that I mean 42−24=18). We know that we want the smaller of them because it's supposed to get bigger when we swap the digits.
So the answer is 24. Easy peasy, right?
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