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# Test the divisibility of the following numbers by 6 a) 5634 b) 65990

**Given: **The numbers are

a) 5634

b) 65990

**To do: **Test the divisibility of the given numbers by 6.

**Solution:**

__Divisibility rule for 6__

If a number ends in a 0, 2, 4, 6 or 8, it is divisible by 2

If a number is such that the sum of its digits is divisible by 3, then the number is divisible by 3.

If a number is divisible by both 2 and 3, then it is divisible by 6.

**a) 5634**

5634 ends in 4. So the number 5634 is divisible by 2.

$5 + 6 + 3 + 4 = 18$. 18 is divisible by 3. So the number 5634 is divisible by 3

As it is divisible both by 2 and 3, **the number 5634 is divisible by 6.**

**
**

**b) 65990**

65990 ends in 0. So the number 65990 is divisible by 2.

$6 + 5 + 9 + 9 + 0 = 29$. 29 is NOT divisible by 3. So the number 65990 is NOT divisible by 3

As it is divisible by 2 but not by 3, the number 65990 is NOT divisible by 6.