 # Exact Divisibility | Divisibility Tests by 2, 3, 4, 5, 6, 7, 8, 9, 10 | Divisibility Rules with Examples

A number is exactly divisible by another number only when it leaves the remainder as 0. Exact Divisibility is also known as perfect divisibility. The solutions are designed by the math experts in Math having vast knowledge about the concepts of exact divisibility.  To find whether a number is perfect divisible or not, we have to apply divisibility tests. Refer to the problems given below to get an idea of Exact divisibility. This helps you to know what is meant by the exact divisibility of a number.

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### Exact Divisibility Tests for 2, 3, 4, 5, 6, 7, 8, 9, 10

Exactly Divisible by 2

A number is said to be exactly divisible by 2 only if the sum of digits is a multiple of 2. The numbers which are exactly divisible by 2 are called even numbers. Let us check the exact divisibility by 2 with the help of some examples.
Example: 12 divided by 2
12 ÷ 2 = 6
Thus 12 is exactly divisible by 2.

Exactly Divisible by 3
If the sum of digits of a number is exactly divisible by 3. Let us see some examples related to the exact divisibility of 3.
Example: 18 divided by 3.
18 is a multiple of 3.
18 ÷ 3 = 6
The quotient is 6 and the remainder is 0.

Exactly Divisible by 4
A number is said to be exactly divisible by 4 only if the sum of digits is a multiple of 4. The numbers which are exactly divisible by 4 are known as even numbers. Let us check the exact divisibility by 4 with the help of some examples.
Example: 48 divided by 4
48 is a multiple of 4.
48 ÷ 4 = 12
The quotient is 12 and the remainder is 0.

Exactly Divisible by 5
A number is divisible by 5 if the number’s last digit is either 0 or 5. Let us see some examples related to divisibility by 5.
Example: 25 divided by 5
25 is a multiple of 5.
25 ÷ 5 = 5
The quotient is 25 and the remainder is 0.

Exactly Divisible by 6
A number is said to be exactly divisible by 6 only if the sum of digits is a multiple of 6. The factors of 6 are 2, 3. If a number is divisible by 2 and 3 then it will be divisible by 6. The numbers which are exactly divisible by 6 are known as even numbers. Let us check the exact divisibility by 6 with examples.
Example: 96 divided by 6
96 is a multiple of 6.
96 ÷ 6 = 16
The quotient is 16 and the remainder is 0.

Exactly Divisible by 7
7 is a prime number. Any number is divisible by 7 if the sum of digits is a multiple of 7. If the difference between twice of the last digit and the number formed by the remaining digits is either 0 or a multiple of 7. For example, twice of 7 is 14 that is divisible by 7.
Example: 49 divided by 7
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56 etc
49 ÷ 7 = 7
The quotient is 7 and the remainder is 0.

Exactly Divisible by 8
The multiples of 8 are even numbers. The numbers that are divisible by 8 will be divisible by 2 and 4. If the sum of digits is multiple of 8 then it will be exactly divisible by 8.
Example: 64 divided by 8
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64 and so on.
64 ÷ 8 = 8
The quotient is 8 and the remainder is 0.

Exactly Divisible by 9
9 is an odd number. The multiples of 9 will be both even and odd numbers. Any number is divisible by 9 if the sum of digits is a multiple of 9. For better understanding let us see some examples related to exact divisibility by 9.
Example: 81 divided by 9
8 + 1 = 9
9 is exactly divisible by 9 that means 81 is divisible by 9.
81 ÷ 9 = 9
The quotient is 9 and the remainder is 0.

Exactly Divisible by 10
A number is divisible by 10 if the number’s last digit is 0. Let us solve some example problems related to divisibility by 10.
Example: 50 divided by 10
50 is a multiple of 10.
50 ÷ 10 = 5
The quotient is 5 and the remainder is 0.

### Problems on Exact Divisibility

Example 1
Find whether 882 is exactly divisible by 9 or not?
Solution:
To know whether 882 is exactly divisible by 9 or not we have to add 3-digits
8 + 8 + 2 = 18
18 has exact divisibility of 9.
It means 882 is divisible by 9.
882 ÷ 9 = 98
Thus 882 is exactly divisible by 9.

Example 2
Find whether the below numbers are divisible by 10.
i. 1985
ii. 2000
iii. 1680
Solution:
i. 1985
Add all the numbers you have to get 0 in the last digit.
1 + 9 + 8 + 5 = 23
23 is not divisible by 10
Thus 1985 is not exactly divisible by 10.

Example 3
Check whether 1009 is divisible by 3.
Solution:
First split the numbers and test the divisibility.
1 + 0 + 0 + 9 = 10
10 is not divisible by 3.
Thus 10 is not exactly divisible by 3.

Example 4:
Find whether 1760 and 1000 are divisible by 2 or not.
Solution:
First split the numbers and test the divisibility.
1760 = 1 + 7 + 6 + 0 = 14
14 is divisible by 2.
1760 ÷ 2 = 880
First split the numbers and test the divisibility.
1000 ÷ 2 = 500
Thus 1760 and 1000 are exactly divisible by 2.

Example 5
Find whether 1260 is divisible by 6 or not.
Solution:
12 and 60 are divisible by 6.
1260 ÷ 6 = 210
Thus 1260 is exactly divisible by 6.

### FAQs on Exact Divisibility

1. What is exact divisibility?

A number is exactly divisible by another number only when it leaves the remainder as 0 when we divide it.

2. Is 18 is exactly divisible by 3?

Sum of the digits = 1 + 8 = 9
9 is exactly divisible by 3.
Thus 18 is exactly divisible by 3.

3. What is the Divisibility Test of 6?

A number is said to be exactly divisible by 6 only if the sum of digits is a multiple of 6. If a number is divisible by 2 and 3 then it will be divisible by 6.

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