Question
A number when divided by 255 gives remainder 40. Find the
remainder when the same number is divided by 15.Solution
ATQ,
Let, the number be ‘N’.
ATQ,
N = 255 × k + 40 = 15 × 17 × k + 15 + 25 = 15 × (17 × k + 1) + 25
Since, 15 × (17 × k + 1) is completely divisible by 15
So, if the number is divided by 15, the remainder will be 25.
If the sum of the digits of a three digit number is subtracted from that number, then it will always be divisible by
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