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Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Example:
1. Let us take the number 42471.
Rule for 9: Sum of the digits of the number is divisible by 9.
Add all the number and divide by 9.
4+2+4+7+1=18 is divisible by 9.
Therefore 42,471 is divisible by 9.
2.Let us take the number 4371.
Rule for 9: Sum of the digits of the number is divisible by 9.
Add all the number and divide by 9.
4+3+7+1=15 is not divisible by 9.
Therefore, 4371 is not divisible by 9.
Divisibility by 10: A number is divisible by 10 if it ends with a 0.
Example:
Let us take a number 1570.
Rule for 10: Number ends with a 0.
Here the last digit is 0.
Therefore, 1570 is divisible by 10
Divisibility by 11: A number is divisible by 11 if the difference of the sums of the alternate digits is0 or a multiple of 11.
Example:
1. Let us take the number 9724.
Rule for 11: Difference of the sums of the alternate digits is0 or a multiple of 11.
Digits in the odd places are: 4 and 7.
Digits in the even places are: 2 and 9.
Sum of the digits in the odd places, 7+4=11.
Sum of the digits in the even places, 9+2=11.
Difference of the sums, 11-11=0.
0 is divisible by 11.
Therefore, 9724 is divisible by 11.
2. Let us take the number 3570.
Rule for 11: Difference of the sums of the alternate digits is0 or a multiple of 11.
Digits in the odd places are: 0 and 5.
Digits in the even places are: 7 and 3.
Sum of the digits in the odd places, 0+5 = 5.
Sum of the digits in the even places, 7+3 = 11.
Difference of the sums, 11-5 = 6.
6 is not divisible by 11.
Therefore, 3570 is not divisible by 11.
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