Question

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

(12) 1,980

Answer 1

We can observe that the digit in the units place is 0.
If a number has either 0 or 5 in its units place, then the number is divisible by 5 and if a number has 0, 2, 4, 6 or 8 in its units place, then the number is divisible by 2. So, the number 1980 is divisible by 2 and 5.

Sum = 1 + 9 + 8 + 0 = 18
It 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 1980 is divisible by 3 and 9.

If a number is divisible by both 2 and 3, then the number is divisible by 6 as well. So, the number 1980 is divisible by 6.

The number formed by the digits in the tens and units places is 80, which is divisible by 4.
If the number formed by the digits in the tens and units places of a number is divisible by 4, then the number is divisible by 4. So, the number 1980 is divisible by 4.

Starting from the right, the digits at odd places are 0 and 9.
Sum = 0 + 9 = 9
The digits at even places are 8 and 1.
Sum = 8 + 1 = 9
Difference between the two sums = 9 – 9 = 0
If the difference between the sums obtained by adding alternate digits of the number is 0 or divisible by 11, then that number is divisible by 11. So, the number 1980 is divisible by 11.

Hence, 1980 is divisible by 2, 3, 4, 5, 6, 9 and 11.