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Question
If 56 × 32y is divisible by 18, find the least value of y.
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Solution
It is given that, the number 56 × 32y is divisible by 18.
Then, it is also divisible by each factor of 18.
Thus, it is divisible by 2 as well as 3.
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.
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