 Divisibility

# 28 Apr Divisibility

At Miracle Learning Centre, we teach you interesting stuff in maths tuition. In this maths tuition, we are going to talk about divisibility. Those of you who have taken some maths tuition on basic arithmetic will already be familiar with the concept of division. Today, we are going to learn about some “good to know” rules about the topic of divisibility. Without wasting any further time, let us get started.

A number say “m” is said to be divisible by another number “n” if m/n leaves no reminders. Let us take an example. The number 8 is divisible by 4 because when 8 is divided by 4, there are no remainders. On the other hand, 8 is not divisible by 5 since in this case, there is a remainder of 3. In this math tuition, we are going to discuss some rules which you could employ to check if a number is divisible by another number.

Divisibility rule for 2

This is a walk in the park. Any even number is divisible by 2. So, if we are told that a number’s last digit is even or 0, we will straight away know that the number will be divisible by 0. Some examples are 1040, 2202 etc.

Divisibility rule for 3

Let’s say we are given the following number and asked whether it is divisible by 3:
3879098088

The number is really big and it seems daunting. There is a very simple rule using which we can figure out whether any number is divisible by 3. For this, first, we will add up all the digits of this number.

3+8+7+9+0+9+8+0+8+8 = 60

The result we get is 60. Now we have to check whether 60 is divisible by 3. Indeed, 60/3 =20 and 60 is divisible by 3. As a result, we can conclude that the number given above is divisible by 3. If the sum were a number not divisible by 3, we could conclude that the number is not divisible by 3.

Divisibility rule for 4

A number is divisible by 4 if the number formed by the last two digits is divisible by 4 . For example, take the number 1085. The number formed by the last two digits of the number is 85. Now, 85 is not divisible by 4 and as a result, we can conclude that 1085 is not divisible by 4. Similarly, the number 1080 is divisible by 4 since the number formed by the last two digits of 1080 which is 80, is divisible by 4.

Divisibility rule for 5

Divisibility rule for 5 is quite simple. If the last digit of a number is 5 or 0, the number is divisible by 5. For example, the number 105, 120 and 2005 – all are divisible by 5. On the other hand, the numbers 103,202,609 are not divisible by 5.

Divisibility rule for 6

A number is divisible by 6 if the number is divisible by 3 as well as 2. For example, let us take the number 618.

To figure out whether 618 is divisible by 6, we will first check if the number is divisible by 2. As we can see, the last digit of the number 618 is 8 which is even. As a result, 618 is divisible by 2.

On the other hand, the sum of the digits of the number 618 = 6+1+8 = 15.

15 is divisible by 3. So 618 is divisible by 3.

As we can see, 618 is divisible by both 2 and 3. As a result, 618 is divisible by 6.
On the other hand, the number 129 will NOT be divisible by 6. Why? This is because although the number 129 is divisible by 3, it is NOT divisible by 2.

Divisibility rule for 7

This one is a bit tricky. Let us see with an example.

Take the number 154 and we are going to test if it is divisible by 7. The last digit of the number is 4. First, we are going to double it by multiplying 2 with it.

4 x 2 =8

Next, we are going to subtract it from the number formed by the rest of the digits. The number formed by the digits except the last digit (which is 4) is 15 in this case. So:

15 – 8 =7
Since the result 7 is divisible by 7, the number 154 is divisible by 7. As a rule, if this result is 0 or is divisible by 7, then we can conclude that the number is also divisible by 7.

Divisibility rule for 8

A number is divisible by 8 if the last three digits of the number are divisible by 8. On the other hand, if a number is divisible by both 4 and 2, then the number is divisible by 8.

Divisibility rule for 9

Divisibility rule for 9 is very similar to the divisibility rule by 3. If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

Divisibility rule for 10

A number is divisible by 10 if the last digit of the number is 0.

Divisibility rule for 11

The divisibility rule for 11 is extremely interesting. Let us see with an example.
Take the number 18453754. In order to figure out whether this number is divisible by 11, we are going to subtract and add the digits alternatively in the following way:

1 -8 + 4 -5 + 3 -7 + 5-4 = -11

As we can see, the result is -11 which is divisible by 11. As a result, we can conclude that 18453754 is divisible by 11. As a rule, if this result is 0 or is divisible by 11, then we can conclude that the original number is also divisible by 11.

We hope you enjoyed this maths tuition from Miracle Learning Centre. Look out for the next math tuition from Miracle Learning Centre.