Divisibility Rule of Four

Vedic Mathematics comprises mathematical tricks for addition, subtraction, multiplication, division, squares, cubes, HCF, and LCM of large numbers. It was founded during AD 1911-1918. Jagadguru Shri Bharathi Krishna Tirthaji was the father of Vedic Mathematics. The divisibility techniques are very useful as we can check whether one number is divisible by another number or not without performing divisions.

Divisibility

Divisibility is a process used to check whether the number when divided by the divisor results in a remainder of 0. The condition for divisibility is that the divisor should not be 0.

Divisibility by 2

For numbers such as 2,4,8, we consider the last digits of the number. Odd numbers aren’t divisible by 2,4,8. A number is said to be divisible by 2 if the last digit of the number is even. That is the last digit should be either 0,2,4,6,8.

Let us illustrate with the help of an example

Consider a number x = 90378. Check the divisibility by 2.

As we can see the last digit of the number is 8.

8 is an even number. It is divisible by 2.

Hence we can conclude that 90378 is divisible by 2.

Divisibility by 4

For a number to be divisible by 4 we have to follow some rules:

• The last two digits of the dividend should either be zero
• Else the last two digits should be considered as a number and this number should be divisible by 4.

Let us illustrate with the help of an example

Consider a number x = 1728900. Check its divisibility by 4 without performing division operations.

We can see the last two digits of 1728900 is 00.

So 0 is divisible by 4.

Hence we can say that 1728900 is divisible by 4.

Let us take another example when the last two digits are not 0

Consider a number x=262898. Check the divisibility by 4.

We can see the last two digits of 262898 is 98.

So 98 is not divisible by 4.

Hence we can say that 262898 is not divisible by 4.

If a number is divisible by 4 then the number is also divisible by 2 as well.

Note

2¹ = 2. The power of 2 is 1. Hence check the divisibility of the last digit by 2.

2² = 4. The power of 2 is 2. Hence check the divisibility of the last two digits of the number by 4.

2³ = 8. The power of 2 is 3. Hence check the divisibility of the last three digits of the number by 8.

Solved Problems

Q1: Check the divisibility 785423696 by 4.

Solution-

The last two digits of the number are 96

96 = 24×4

Hence we can say that 785423696 is divisible by 4.

Q2: Find the values that b can take such that 17238b is divisible by 4.

Solution-

As we all know that the last 2 digits should be divisible by 4.

The last two digits are 8b. So the values b can take to make the whole number divisible by 4 are 0, 4, 8.

80 is divisible by 4.

84 is divisible by 4.

88 is divisible by 4.

Therefore the values of b are 0,4,8.

Q3: Check whether 7899 is divisible by 4 or not

Solution-

We can see that 7899 is an odd number.

Odd numbers are not divisible by 2,4,6,8.

Hence 7899 is not divisible by 4.

Q4: Check the divisibility 18524 by 4.

Solution-

The last two digits of the number are 24

24 = 6×4

Hence we can say that 18524 is divisible by 4.

Q5: Consider a number x = 89642585585552222232. Check the divisibility by 2.

Solution-

As we can see the last digit of the number is 2.

2 is an even number .

It is divisible by 2.

Hence we can conclude that 89642585585552222232 is divisible by 2.