In order to understand divisibility, you need to understand what division means. In simple words, division means to divide two numbers in maths. For example, we have two numbers, they are number a and number b. If we are dividing b by a, it means that we are finding how many a parts are available in the b. That is called division. It is written in this form.

(4 \times 6) + 0 = 24

Where 4 is the divisor,

6 is the quotient,

0 is the remainder,

and 24 is the dividend.

 

However, divisibility is something else. It is derived from division but there is a twist in it. Divisibility says that if two numbers (let's say a and b) are divided, the division should be exact. This means that the remainder should be equal to zero. You might be wondering that this means the above example is also an example of divisibility? The answer is yes! It is also an example of divisibility because if you look carefully, the remainder is zero. The only difference between division and divisibility is that division can give you a remainder and that is fine but not in the case of divisibility because divisibility says the remainder should always be zero.

Rules of Divisibility

There are some rules of divisibility. Although the condition will remain the same (which is the remainder should always be zero), however, when you are finding divisible of different numbers, these rules can come in handy.

Divisible by 2

A number is divisible by 2 if its last digit is a zero or an even number.

24, 238, 1,024

Divisible by 3

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

564

5 + 6 + 4 = 15, is multiple 3

2,040

2 + 0 + 4 + 0 = 6, is multiple 3

Divisible by 5

A number is divisible by 5, if it ends in zero or five.

45, 515, 7,525

Divisible by 7

A number is divisible by 7 when the difference between the number without the figure of the units and the double the number of the units is 0 or a multiple of 7.

343

34 - 2 \times 3 = 28, is multiple of 7.

105

10 - 5 \times 2 = 0

2261

226 - 1 \times 2 = 224.

Repeat the process with 224.

22 - 4 \times 2 = 14, is multiple of 7.

Divisible of 11

A number is divisible by 11 if the difference between the sum of the figures who occupy the even numbers and the odd numbers is 0 or a multiple of 11.

121

(1 + 1) - 2 = 0

4,224

(4 + 2) - (2+4) = 0

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Other rules

Divisible by 4

A number is divisible by 4 if the last two digits are zeros or a multiple of 4.

36, 400, 1,028

Divisible by 6

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

72, 324, 4,200

Divisible by 8

A number is divisible by 8 if its last three figures are zeros or a multiple of 8.

4000, 1048, 1512

Divisible by 9

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

81

8 + 1 = 9

3,663

3 + 6 + 6 + 3 = 18, is multiple of 9

Divisible by 10

A number is divisible by 10 if the last figure in the unit is 0.

130, 1,440, 10,230

Divisible by 25

A number is divisible by 25 if their last two digits are zeros or a multiple of 25.

500, 1,025, 1,875

Divisible by 125

A number is divisible by 125 if its last three figures are zeros or a multiple of 125.

1,000, 1,125, 4,250

Factoring

Factoring a number into prime factors is to express the number as a product of prime numbers.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.