Question

How to solve this question ? ​

Answer 1

Step-by-step explanation:

Since 110=2⋅5⋅11110=2⋅5⋅11 is the product of three distinct primes, the only way a product of four integers is 110110 is when they are 1,2,5,111,2,5,11.

Indeed, take the largest of the four numbers: it must be a divisor of 110110, so it is among 1,2,5,10,11,22,55,1101,2,5,10,11,22,55,110. However, 22,55,11022,55,110 don’t leave space for other three distinct divisors with a product of 110110. On the other hand, the largest cannot be 1010 or less, because the product has to contain the factor 1111. Then take the largest number in the remaining three, whose product is 1010 and see it must be 55. Hence the other two have to be 2.2

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