Divisibility Rules for Whole Numbers

Divisibility rules are a set of guidelines that help us determine whether a whole number is divisible by another whole number without performing the actual division. These rules are useful for simplifying calculations, checking answers, and solving problems in mathematics.

Divisibility Rules

1. Divisibility by 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

Example: 18, 24, 30, 42, 56

2. Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Example: 18 (1 + 8 = 9), 27 (2 + 7 = 9), 36 (3 + 6 = 9)

3. Divisibility by 4

A number is divisible by 4 if the last two digits form a number that is divisible by 4.

Example: 100, 104, 108, 112, 120

4. Divisibility by 5

A number is divisible by 5 if its last digit is either 0 or 5.

Example: 10, 15, 20, 25, 30

5. Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

Example: 12, 18, 24, 30, 36

6. Divisibility by 7

A number is divisible by 7 if the difference between twice the digit at the unit’s place and the number formed by the remaining digits is divisible by 7.

Example: 14 (2 × 4 - 1 = 7), 21 (2 × 1 - 2 = 0)

7. Divisibility by 8

A number is divisible by 8 if the last three digits form a number that is divisible by 8.

Example: 1000, 1008, 1016, 1024, 1032

8. Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Example: 18 (1 + 8 = 9), 27 (2 + 7 = 9), 36 (3 + 6 = 9)

 

9. Divisibility by 10

A number is divisible by 10 if its last digit is 0.

Example: 10, 20, 30, 40, 50

 

Practice Questions

1. Which of the following numbers is divisible by 2?

a) 15                      b) 22                      c) 31                      d) 43

 

2. Which of the following numbers is divisible by 3?

a) 12                      b) 15                      c) 18                      d) 21

 

3. Which of the following numbers is divisible by 4?

a) 100                    b) 104                    c) 108                    d) All of the above

 

4. Which of the following numbers is divisible by 5?

a) 10                      b) 15                      c) 20                      d) All of the above

 

5. Which of the following numbers is divisible by 6?

a) 12                      b) 18                      c) 24                      d) All of the above 

Answer Key

1	2	3	4	5
(b) 22	(c) 18	(d) All of the above	(d) All of the above	(d) All of the above

Conclusion

Divisibility rules are a useful tool for simplifying calculations and solving problems in mathematics. By applying these rules, we can quickly determine whether a whole number is divisible by another whole number without performing the actual division.

pdf of this notes is available -https://t.me/cgscbsesupportbypramodsir/44