Divisibility Rule of 4

The divisibility rule of 4 is a simple mathematical rule or test that is used to determine whether a given integer is divisible by 4 or not without performing the actual division. It saves time by checking the divisibility of a number by 4 without doing the actual division.

This rule states that either the last two digits of the dividend should be zero or the last two digits should be considered as a number and this number should be divisible by 4.

For Example:
Check if 1248 is divisible by 4.
The last two digits are 48.
48 ÷ 4 = 12 (which is a whole number)

Since 48 is divisible by 4, 1248 is divisible by 4.

More Examples on Divisibility Rule of 4

1. 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.

2. 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.

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

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.

Divisibility Rule of 4 Proof

We have, N = 10ⁿ a_n + 10^n-1 a_n-1 + 10^n-2 a_n-2 + ⋯+ 10² a₂ + 10 a₁ + a₀

Taking mod 4 of N, we get

N ≡ 0 + 0 + 0 +⋯+ 0 + 10a₁ + a₀ (mod 4) (as 10k, where k ≥ 2, is always divisible by 4)​ ≡ 10a₁ + a₀ (mod 4).

Therefore, N ≡ 0(mod 4) if 10a₁ + a₀ = \overline {a_1a_2} ≡ 0(mod 4).

So, If the tens and units places of a number taken in that order are divisible by 4, then the number is also divisible by 4.

Solved Questions on Divisibility Rule of 4

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.

Check Other Divisibility Rules:

• Divisibility Rule of 2
• Divisibility Rule of 3
• Divisibility Rule of 6
• Divisibility Rule of 7
• Divisibility Rule of 9

Divisibility Rule of 4 Worksheet

1. Is the number 1238 divisible by 4?

2. Determine whether 4567 is divisible by 4.

3. Check if the number 9876 is divisible by 4.

4. Is the number 1420 divisible by 4?

5. Determine if 3050 is divisible by 4.

6. Find out if the number 6789 is divisible by 4.

7. Is the number 244 divisible by 4?

8. Check if 1024 is divisible by 4.

Also Check: Practice Questions on Divisibility Rules