Divisibility rule of 2 – – A number is divisible by 2 if the last digit of the number is 0, 2, 4, 6, or 8

e.g. 256 is divisible by 2 because last digit is divisible by 2

______________________________________________

Divisibility rule of 3 – – If the sum of the digits of a number is divisible by 3, then the number is divisible by 3

e.g. 345 is divisible by 3 because sum of digits is 3+4+5=12 which is divisible by 3

______________________________________________

Divisibility rule of 4 – – The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4.

e.g. 144 is divisible by 4 because last 2 digits 44 are divisible by 4

______________________________________________

Divisibility rule of 5 – – Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5

e.g. 195 is divisible by 5 because last digit is 5

______________________________________________

Divisibility rule of 6 – – A number is divisible by 6 if it is divisible by 2 and 3 both.

e.g. 72 is divisible by both 2 and 3 hence is divisible by 6

______________________________________________

Divisibility rule of 7 – – Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7.

e.g. 1015 is divisible by 7

Take the last digit 5 and double it (10). Remaining number is 101.now subtract 10 from 101 which is 91.again do the same process

Take 1 from 91 and double it which is 2 and subtract 2 from 9 = 7 which is divisible by 7 hence the number 1015 is divisible by 7

______________________________________________

Divisibility rule of 8 – – A number is divisible by 8 if the numbers formed by the last three digits is divisible by 8.

e.g. 19640 divisible by 8 because last three digits 640 are evenly divided by 8

______________________________________________

Divisibility rule of 9 – – If the sum of the digits of a number is divisible by 9, then the number is divisible by 9

e.g. 93987 is divisible by 9 because sum of its digits 9+3+9+8+7 = 36 is divisible by 9

______________________________________________

Divisibility rule of 10 – – If a number ends in a 0, it is divisible by 10. Also if a number is divisible by both 2 and 5, it is divisible by 10.

e.g. 10000 is divisible by 10 because it is divisible by both 2and 5 and it also ends with 0.

______________________________________________

Divisibility rule of 11 – – Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number

e.g. 50237 is divisible by 11 because 5-0+2-3+7 = 11 which is divisible by 11

## Answers ( )

2:–The number should end with 0, 2, 4, 6 or 8.

ex, 252, 468

3:–The digits of the number should add up to a multiple of 3.

ex, 261 ≈ 2+6+1 = 9

4:–The last two digits of the no. should be a multiple of 4.

ex, 128, 240

5:–The no. should end with 5 or 0.

ex, 10, 15

6:–The no. should be divisible by both 2 and 3.

ex, 522, 60

7:–There is no divisibility rule of 7.

8:–The last three digits should be a multiple of 8.

ex, 4800, 1648

9:–The digits of the number should add up to a multiple of 9.

ex, 81, 369

10:–The no. should end with 0.

ex, 20, 360

11:–(The sum of digits on odd place)-(The sum of digits on even place) should be = 11’s multiple.

ex, 22 ≈ 2 – 2 = 0

Step-by-step explanation:______________________________________________

Divisibility rule of 2 – – A number is divisible by 2 if the last digit of the number is 0, 2, 4, 6, or 8

e.g. 256 is divisible by 2 because last digit is divisible by 2

______________________________________________

Divisibility rule of 3 – – If the sum of the digits of a number is divisible by 3, then the number is divisible by 3

e.g. 345 is divisible by 3 because sum of digits is 3+4+5=12 which is divisible by 3

______________________________________________

Divisibility rule of 4 – – The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4.

e.g. 144 is divisible by 4 because last 2 digits 44 are divisible by 4

______________________________________________

Divisibility rule of 5 – – Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5

e.g. 195 is divisible by 5 because last digit is 5

______________________________________________

Divisibility rule of 6 – – A number is divisible by 6 if it is divisible by 2 and 3 both.

e.g. 72 is divisible by both 2 and 3 hence is divisible by 6

______________________________________________

Divisibility rule of 7 – – Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7.

e.g. 1015 is divisible by 7

Take the last digit 5 and double it (10). Remaining number is 101.now subtract 10 from 101 which is 91.again do the same process

Take 1 from 91 and double it which is 2 and subtract 2 from 9 = 7 which is divisible by 7 hence the number 1015 is divisible by 7

______________________________________________

Divisibility rule of 8 – – A number is divisible by 8 if the numbers formed by the last three digits is divisible by 8.

e.g. 19640 divisible by 8 because last three digits 640 are evenly divided by 8

______________________________________________

Divisibility rule of 9 – – If the sum of the digits of a number is divisible by 9, then the number is divisible by 9

e.g. 93987 is divisible by 9 because sum of its digits 9+3+9+8+7 = 36 is divisible by 9

______________________________________________

Divisibility rule of 10 – – If a number ends in a 0, it is divisible by 10. Also if a number is divisible by both 2 and 5, it is divisible by 10.

e.g. 10000 is divisible by 10 because it is divisible by both 2and 5 and it also ends with 0.

______________________________________________

Divisibility rule of 11 – – Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number

e.g. 50237 is divisible by 11 because 5-0+2-3+7 = 11 which is divisible by 11

______________________________________________