Question

Use the divisibility tests to determine whether the following numbers are divisible by 2, 3, 4, 5, 6, 9 or 11.

(1) 99

Answer 1

We can observe that the sum of the digits 9 and 9 is 18, which is divisible by both 3 and 9.
We know that if the sum of all the digits in a number is divisible by 3 and 9, then the number is divisible by both 3 and 9. So, the number 99 is divisible by both 3 and 9.

Starting from the right, the digit at odd place is 9 and the digit at even place is 9.
Difference between the two = 9 – 9 = 0
We know that if the difference between the sums obtained by adding alternate digits of a number is 0 or divisible by 11, then the number is divisible by 11. So, the number 99 is divisible by 11.

Hence, the number 99 is divisible by 3, 9 and 11.