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Question 74

If 56x32y is divisible by 18, find the least value of y.


Solution

It is given that, the number 56x32y is divisible by 18. Then, it is also divisible by each factor of 18.
Thus, it is divisible by 2, 3 as well as 9.
Now, the number is divisible by 2, its unit's digit must be an even number that is 0, 2, 4, 6, ......
Therefore, the least value of y is 0.
Again, the number is divisible by 3 also, sum of its digits is a multiple of 3.
i.e.  5 + 6 + x + 3 + 2 + y is a multiple of 3.
16 + x + y = 0, 3, 6, 9, .......
16 + x = 18
x = 2, which is the least value of x.
Again, the number is divisible by 9 also, the sum of its digits is a multiple of 9.
i.e.  5 + 6 + x + 3 + 2 + y is a multiple of 9.
16 + x + y = 0, 9, 18 .......
16 + x = 18
x = 2, which is the least value of x.

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