Divisibility Rules are important (and easy as well) because these are useful in questions of Number System asked in Various Exams. To know if a number is divisible by another number or not, we must know these rules. Divisibility Rules help you know whether a number is divisible by another number (leaving no remainder) without actually doing the division. In this post, I will explain you these Rules in the simplest manner so that you can understand them well and use to solve your questions easily, precisely and quickly.

A number is divisible by 2 if its unit digit (last digit) is any of 0, 2, 4, 6, 8, i.e., if the last digit is even the number is also even (divisible by 2).

Ex. The number

If the sum of all digits of a number is divisible by 3, the number is also divisible by 3.

Note : This rule can be repeated if needed.

Ex. Check if 57426 is divisible by 3.

To check its divisibility by 3, we will take sum of its digits,

5 + 7 + 4 + 2 + 6 = 24

24, which is divisible by 3, means the number 57426 is also divisible by 3.

Lets take one more example, 48952, check the number's divisibility by 3.

Add all of its digits,

4 + 8 + 9 + 5 + 2 = 28

28, which is not divisible by 3, so the number 48952 is also not divisible by 3.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Ex. Which of the following numbers are divisible by 4?

(a) 745256 (b) 58274 (c) 847326 (d) 28976

Explanation: (a) number by last two digits, 56, is divisible by 4, so the number 745256 is divisible by 4.

(b) as 74, number formed by last two digits, is not divisible by 4, the original number 58274 is not divisible 4.

(c) 26 is not divisible by 4, so again 847326 is not divisible by 4.

(d) here 76 is divisible by 4, so this number 28976 is divisible by 4.

If the unit digit of a number is either 5 or 0, the number is divisible by 5, otherwise it's not.

Ex. Numbers like 15, 70, 145, 8795, 2530 are divisible by 5 as their unit's digit is either 5 or 0, but number like 4582, 723, 189, 76 are not divisible by 5.

To know whether a number is divisible by 7 or not, we will double the unit digit of the number and subtract it from the number formed by rest digits, if the result is divisible by 7, the number is also divisible by 7. In case, there is still doubt about the result number repeat the process (this rule can be repeated if needed) till you know.

Ex. Out of four numbers given below, choose the one divisible by 7?

(a) 4852 (b) 7105 (c) 6905 (d) 8762

Solution: (a) the number is 4852

as per rule mentioned above, take the last digit, double it, and subtract from rest of the number 485 - 4 = 481

again, 48 - 2 = 46 which is not divisible by 7,

means 481 is not divisible by 7 and 4852 is also not divisible 7.

(b) 7105,

again going as the rule, 710 - 10 = 700, which is divisible by 7, so the number 7105 is divisible by 7.

We can check rest two as well, but now as we know that option (b) '7105' is the answer, we can skip them.

A number is divisible by 8 if the number formed its last three digits, i.e., hundred's, ten's and unit's digit, is divisible by 8.

This rule is similar to the Divisibility Rule of 4, the only difference is that we have to check on the number formed by last three digits instead of two, and will divide them by 8.

If the sum of all digits of a number is divisible by 9, the number is also divisible by 9.

Note : This rule can be repeated if needed.

A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its places at even places is either 0 or a number divisible by 11.

In this method, to check the divisibility of a number by 11, we will subtract the its last digit from the number formed by rest of the digits, if the result is divisible by 11, the original number is, too. We can repeat the process if needed.

**Divisibility by 2:**A number is divisible by 2 if its unit digit (last digit) is any of 0, 2, 4, 6, 8, i.e., if the last digit is even the number is also even (divisible by 2).

Ex. The number

*58476*is divisible by*2*as its last digit is*6*and the number*24731*is not divisible by*2*as its last digit is*1*(not even).**Divisibility by 3:**If the sum of all digits of a number is divisible by 3, the number is also divisible by 3.

Note : This rule can be repeated if needed.

Ex. Check if 57426 is divisible by 3.

To check its divisibility by 3, we will take sum of its digits,

5 + 7 + 4 + 2 + 6 = 24

24, which is divisible by 3, means the number 57426 is also divisible by 3.

Lets take one more example, 48952, check the number's divisibility by 3.

Add all of its digits,

4 + 8 + 9 + 5 + 2 = 28

28, which is not divisible by 3, so the number 48952 is also not divisible by 3.

**Divisibility by 4:**A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Ex. Which of the following numbers are divisible by 4?

(a) 745256 (b) 58274 (c) 847326 (d) 28976

Explanation: (a) number by last two digits, 56, is divisible by 4, so the number 745256 is divisible by 4.

(b) as 74, number formed by last two digits, is not divisible by 4, the original number 58274 is not divisible 4.

(c) 26 is not divisible by 4, so again 847326 is not divisible by 4.

(d) here 76 is divisible by 4, so this number 28976 is divisible by 4.

**Divisibility by 5:**If the unit digit of a number is either 5 or 0, the number is divisible by 5, otherwise it's not.

Ex. Numbers like 15, 70, 145, 8795, 2530 are divisible by 5 as their unit's digit is either 5 or 0, but number like 4582, 723, 189, 76 are not divisible by 5.

**Divisibility by 7:**To know whether a number is divisible by 7 or not, we will double the unit digit of the number and subtract it from the number formed by rest digits, if the result is divisible by 7, the number is also divisible by 7. In case, there is still doubt about the result number repeat the process (this rule can be repeated if needed) till you know.

Ex. Out of four numbers given below, choose the one divisible by 7?

(a) 4852 (b) 7105 (c) 6905 (d) 8762

Solution: (a) the number is 4852

as per rule mentioned above, take the last digit, double it, and subtract from rest of the number 485 - 4 = 481

again, 48 - 2 = 46 which is not divisible by 7,

means 481 is not divisible by 7 and 4852 is also not divisible 7.

(b) 7105,

again going as the rule, 710 - 10 = 700, which is divisible by 7, so the number 7105 is divisible by 7.

We can check rest two as well, but now as we know that option (b) '7105' is the answer, we can skip them.

**Divisibility by 8:**A number is divisible by 8 if the number formed its last three digits, i.e., hundred's, ten's and unit's digit, is divisible by 8.

This rule is similar to the Divisibility Rule of 4, the only difference is that we have to check on the number formed by last three digits instead of two, and will divide them by 8.

**Divisibility by 9:**If the sum of all digits of a number is divisible by 9, the number is also divisible by 9.

Note : This rule can be repeated if needed.

**Divisibility by 11:**A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its places at even places is either 0 or a number divisible by 11.

**Another Rule for 11:**In this method, to check the divisibility of a number by 11, we will subtract the its last digit from the number formed by rest of the digits, if the result is divisible by 11, the original number is, too. We can repeat the process if needed.

**Note:**If a number is divisible by two prime numbers, it is also divisible by their product.

For example, if a number is divisible by both 2 and 3, it is also divisible by their product, i.e., 6. Again if a number is divisible by both 3 and 7, it is also divisible by 21.

So to check the divisibility of number by 6, we have to check its divisibility by 2 and 3 both.

Again to check the divisibility of a number by 15, we will check its divisibility by 3 and 5.

In upcoming post we will discuss questions from Number System and Divisibility Rules asked in various Exams.

Again to check the divisibility of a number by 15, we will check its divisibility by 3 and 5.

In upcoming post we will discuss questions from Number System and Divisibility Rules asked in various Exams.