Question

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

(6) 495

Answer 1

We can observe that the sum of the digits is 4, 9 and 5 is 18, which is divisible by both 3 and 9.
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 495 is divisible by both 3 and 9.

Also, the number has the digit 5 in its units place.
If a number has either 0 or 5 in its units place, then the number is divisible by 5. So, the number 495 is divisible by 5.

Starting from the right, the digits at odd places are 5 and 4.
Sum = 5 + 4 = 9
The digit at even place is 9.
Difference between the sums = 9 – 9 = 0
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 495 is divisible by 11.

Hence, the number 495 is divisible by 3, 5, 9 and 11.