Shortcuts for Divisibility by 10,11, 12 and 15

Divisibility by 10:
How to check a number is divisible by 10?
It is very simple, check for the units digit of the number, if it is 0, then the number is clearly divisible by 10.

Examples:
Is the number 1234567890 divisible by 10?
Check for the unit digit, it is 0,
5 + 7 + 2 + 2 + 5 + 8 + 3 + 4 = 36
So 1234567890 is divisible by 10.

Is the number 1236985 divisible by 10?
The unit digit is not zero, so the number 1236985 is not divisible by 10.

Divisibility by 11:
How to check a number is divisible by 11?
It is very simple, check the number, if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.

Examples:
Is the number 2547039 divisible by 11?
First find the difference between sum of its digits at odd and even places.
(Sum of digits at odd places) – (Sum of digits at even places)
= (9 + 0 + 4 + 2) – (3 + 7 + 5)
= 15 – 15 = 0
The number is 0, so the number 2547039 is divisible by 11.

Is the number 13165648 divisible by 11?
(Sum of digits at odd places) – (Sum of digits at even places)
= (8 + 6 + 6 + 3) – (4 + 5 + 1 + 1)
= 23 – 11 = 12
The number is 12, so the number 13165648 is not divisible by 11.

Divisibility by 12:
How to check a number is divisible by 12?
It is very simple, check the number is divisible by 3 and 4, if it is divisible by both, then clearly the number is divisible by 12.

Examples:
Is the number 59175432 divisible by 12?
First check the number is divisible by 3,
5 + 9 + 1 + 7 + 5 + 4 + 3 + 2 = 36
36 is divisible by 3, so the number is also divisible by 3.
Then check the number is divisible by 4 also,
The last two digit of the number is 32.
32 is divisible by 4, so the number is also divisible by 4.
The number 59175432 is divisible both by 3 and 4, so it is divisible by 12.

Is the number 39737094 divisible by 12?
3 + 9 + 7 + 3 + 7 + 0 + 9 + 4 = 42.
42 is divisible by 3, so the number is also divisible by 3.
Now check the number is divisible by 4 also,
The last two digit of the number is 94.
94 is not divisible by 4, so the number is not divisible by 4
The number 39737094 is divisible only by 3 and not by 4, so it is not divisible by 12

Divisibility by 15:
How to check a number is divisible by 15?
It is very simple, check the number is divisible by 3 and 5, if it is divisible by both, then clearly the number is divisible by 15.

Examples:
Is the number 469192440 divisible by 15?
First check the number is divisible by 3,
4 + 6 + 9 + 1 + 9 + 2 + 4 + 4 + 0 = 39
39 is divisible by 3, so the number is also divisible by 3.
Then check the number is divisible by 5 also,
Check the units digit in the given number
unit digit is 0, so the number is also divisible by 5.
The number 469192440 is divisible both by 3 and 5, so it is divisible by 15.

Is the number 326643 divisible by 15?
3 + 2 + 6 + 6 + 4 + 3 = 24.
24 is divisible by 3, so the number is also divisible by 3.
Now check the number is divisible by 5 also,
The units digit is not 0 or 5, so the number is not divisible by 5
The number 326643 is divisible only by 3 and not by 5, so it is not divisible by 15.S

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