# Divisibility Rules for numbers 21 to 29

### Divisibility Rules for numbers 21 – 29

The divisibility rules for numbers 21 to 29 test whether any of the numbers 21 to 29 is a divisor of a given number. That is, given any number, you should be able to check or ascertain that the number is divisible by a number between 20 and 30. Below are the rules

#### The rule for number 21:

(a) A number N is divisible by 21 if the difference between the remaining number and 2 times the last digit is 0 or a number divisible by 21

(b) A number N is divisible by 21 if the difference between 11 times the remaining number and the last digit is 0 or a number divisible by 21.

(c) A number N is divisible by 21 if the sum of 3 times the last digit and 9 times the remaining number is a number divisible by 21

Examples:

Example (a): Test whether 1029 is divisible by 21,                                                                                             102 – (2×9) = 102 – 18 = 84, a number divisible by 21.

Example (b): Test whether 42 is divisible by 21,                                                                                                 42:  (11 x 4) – 2 = 42 = 2 x 21

Example (c): Test whether 126 is divisible by 21,                                                                                              126: 9 x 12 + 3 x 6 = 126 = 21 x 6

#### The Rule for number 22

(a) A number N is divisible by 22 if the difference between 12 times the remaining number and the last digit is 0 or a number divisible by 22.

(b) A number N is divisible by 22 if the difference between twice the remaining number and 2 times the last digit is 0 or a number divisible by 22.

(c) A number N is divisible by 21 if the sum of 3 times the last digit and 8 times the remaining number is a  number divisible by 22.

Examples for Rule 22

Example (a) Subtracting the last digit from 12 times the rest, gives a multiple of 22,                                              110:  (12 x 11) – 0 = 132 = 22 x 6

Example (b) Subtracting twice the last digit from twice the rest, gives a multiple of 22,                                         132: 2 x 13 – 2 x 2 = 22 = 1 x  22

Example (c) Adding 3 times the last digit to 8 times the rest, gives a multiple of 22,                                          132: 8 x 13 + 3 x 2 = 110 = 22 x 5

#### The Rule for number 23

(a) A number N is divisible by 23 if the sum of 7 times the remaining number minus 3 times the last digit is a number divisible by 23.

(b) A number N is divisible by 23 if the difference between 13 times the remaining number and the last digit is 0 or a number divisible by 23

(c) A number N is divisible by 23 if the difference between of 3 times the remaining number and 2 times the last digit is a number divisible by 23.

Examples for Rule 23

Example (a) Add 3 times the last digit to 7 times the rest,                                                                                    92: 7 x 9 + 3 x 2 = 69 = 23 x 3

Example (b) Subtract the last digit from 13 times the rest,                                                                                 46:  (13 x 4) – 6 = 46 = 23 x 2

Example (c) Subtract twice the last digit from three times the rest,                                                                    138: 3 x 13 – 2 x 8 = 23 = 1 x 23

#### The rule for number 24

(a) A number N is divisible by 24 if 14 times the remaining number minus the last digit is a number divisible by 24.

(b) A number N is divisible by 24 if the difference between 4 times the remaining number and 2 times the last digit is a number divisible by 24.

(c) A number N is divisible by 24 if the sum of 6 times the remaining number and 3 times the last digit is a number divisible by 24.

Examples for Rule 24

Example (a) Test whether 48 is divisible by 24 by using  rule 24(a)                                                                    48:  (14 x 4) – 8 = 48 = 24 x 2

Example (b) Test whether 168 is divisible by 24 by using  rule 24(b)                                                                168: 4 x 16 – 2 x 8 = 48 = 2 x 24

Example (c) Test whether 144 is divisible by 24 by using  rule 24(c)                                                                 144: 6 x 14 + 3 x 4 = 96 = 24 x 4

#### The rule for number 25:

(a) A number N is divisible by 25 if the difference between 15 times the remaining number and the last digit is 0 or a number divisible by 25.

(b) A number N is divisible by 25 if the sum of 5 times the remaining number and the 3 times the last digit is a number divisible by 25.

(c) A number N is divisible by 25 if the difference between 5 times the remaining number and 2 times the last digit is 0 or a number divisible by 25.

Examples for Rule 25

Example (a)  Test whether 75 is divisible by 25 by using rule 25(a)                                                                    75:  (15 x 7) – 5 = 100 = 25 x 4

Example (b) Add 3 times the last digit to 5 times the rest,                                                                                  175: 5 x 17 + 3 x 5 = 100 = 25 x 4

Example (c) Subtract twice the last digit from 5 times the rest,                                                                         125: 5 x 12 – 2 x 5 = 50 = 2 x 25

#### The rule for number 26

(a) A number N is divisible by 26 if the sum of 6 times the remaining number minus 2 times the last digit is a number is divisible by 26.

(b) A number N is divisible by 26 if the sum of 4 times the remaining number and 3 times the last digit is a number is divisible by 26.

(c) A number N is divisible by 26 if the difference between 16 times the remaining number and the last digit is 0 or a number divisible by 26.

Examples for Rule 26

Example (a)  Test whether 104 is divisible by 26 by using rule 26(a)                                                                  104: 6x 10 – 2 x 4 = 52 = 2 x 26

Example (b)  Test whether 156 is divisible by 26 by using rule 26(b)                                                                  156: 4 x 15 + 3 x 6 = 78 = 26 x 3

Example (c)  Test whether 52 is divisible by 26 by using rule 26(c)                                                                    52:  (16 x 5) – 2 = 78 = 26 x 3

#### The rule for number 27

(a) A number N is divisible by 27 if the difference between 17 times the remaining number and the last digit is 0 or a number divisible by 27.

(b) A number N is divisible by 27 if 7 times the remaining number minus 2 times the last digit is a number divisible by 27.

(c) A number N is divisible by 27 if the sum of 3 times the last digit and 3 times the remaining number is a number divisible by 27.

Examples for Rule 27

Example (a)  Test whether 54 is divisible by 27 by using rule 27(a)                                                                   54:  (17 x 5) – 4 = 81 = 27 x 3

Example (b)  Test whether 108 is divisible by 27 by using rule 27(b)                                                                108: 7 x 10 – 2 x 8 = 54 = 2 x 27

Example (c)  Test whether 135 is divisible by 27 by using rule 27(c)                                                                 135: 3 x 13 + 3 x 5 = 54 = 27 x 2

#### The Rule for number 28

(a) A number N is divisible by 28 if the sum of the last digit and 3 times the remaining number is divisible by 28.

(b) A number N is divisible by 28 if 18 times the remaining number minus the last digit is divisible by 28.

(c) A number N is divisible by 28 if the difference between 8 times the remaining number and twice the last digit is 0 or a number divisible by 28.

Examples for Rule 28

Example (a)Test whether 168 is divisible by 28                                                                                                    68: 2 x 16 + 3 x 8 = 56 = 28 x 2

Example (a) Test whether 56 is divisible by 28                                                                                                         56:  (18 x 5) – 6 = 84 = 28 x 3

Example (a) Test whether 84 is divisible by 28                                                                                                       84: 8 x 8 – 2 x 4 = 56 = 28 x 2

#### The Rule for number 29

(a) A number N is divisible by 29 if the difference between 19 times the remaining number and the last digit is a number is divisible by 29.

(b) A number N is divisible by 29 if the difference between 9 times the remaining number and the 2 times the last digit is 0 or a number divisible by 29.

Examples for Rule 29

Example (a) Subtract the last digit from 19 times the rest, gives a multiple of 29,                                                  58:  (19 x 5) – 8 = 87 = 29 x 3

Example (b) Test whether 87 is divisible by 29 by subtracting twice the last digit from 9 times the rest,                 87: 9 x 8 – 2 x 7 = 58 = 2 x 29