# number of values of 'a'(from 0 to 9) for which the no N = 2345631143a4 is divisible by 12 is: 0, 1, 2,more than 2 i know the ans is 2.. plz explain.thanks in advance

30 Points
13 years ago

Dear Jayati,

Solution:- For the number to be divisible by 12, it has to be divisible by 4 and 3.

Divisibility criteria for 3: Sum of the digits of the number should be divisible by 3.

Sum of the digits of N = a + 36

Since, 36 is divisible by 3. So, for N to be divisible by 3, 'a' can have following values- 0, 3, 6, or 9.

Now, Divisibility criteria for 4: The last 2 digits of the number should be divisible by 4. In our case, 'a4' should be divisible by 4.

'a4' can be 04, 34, 64, or 94. From these 4 values, only 4 and 64 are divisible by 4. Therefore, 'a' can be either 0 or 6.

ANS = 2

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