Given that the number \(\overline{35a64}\) is divisible by 3, where a

1.	Given that the number \(\overline{35a64}\) is divisible by 3, where a is a digit, what are the possible values of a?
Answer» Here it is given that \(\overline{35a64}\) is divisible by 3. We know that if a number is divisible by 3, then sum of digits must be a multiple of 3. ∴ 3 + 5+a+6+4 = multiple of 3 ∴ a + 18 = 0,3,6,9,12,15,….. But ‘a’ is a digit, hence, ‘a’ can have value between 0 to 9. ∴ a + 18 = 18 which gives a = 0. ∴ a + 18 = 21 which gives a = 3. ∴ a + 18 = 24 which gives a = 6. ∴ a + 18 = 27 which gives a = 9. ∴ a = 0,3,6,9

Given that the number \(\overline{35a64}\) is divisible by 3, where a is a digit, what are the possible values of a?

Answer»

Here it is given that \(\overline{35a64}\) is divisible by 3.

We know that if a number is divisible by 3, then sum of digits must be a multiple of 3.

∴ 3 + 5+a+6+4 = multiple of 3

∴ a + 18 = 0,3,6,9,12,15,…..

But ‘a’ is a digit, hence, ‘a’ can have value between 0 to 9.

∴ a + 18 = 18 which gives a = 0.

∴ a + 18 = 21 which gives a = 3.

∴ a + 18 = 24 which gives a = 6.

∴ a + 18 = 27 which gives a = 9.

∴ a = 0,3,6,9