Divisibility Rule of 4: Rules, Tricks and Examples

Divisibility Rule of 4 checks whether a number can be divided by 4 without leaving a remainder. For any whole number, examine its last two digits: if that two-digit number is divisible by 4, the entire number is divisible by 4. This page explains the rule, shortcut method, examples and common cases.

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What is the Divisibility Rule of 4?

A number is divisible by 4 if its last two digits form a number divisible by 4. The division must give a whole-number quotient and remainder 0.

This rule works because every number can be written as 100q + r, where r is the number formed by its last two digits. Since 100 is divisible by 4, 100q is also divisible by 4. Therefore, divisibility depends only on r. For example, the last two digits of 2,316 are 16, and 16 is divisible by 4, so 2,316 is divisible by 4.

Divisibility Rule of 4 Formula & Tricks

Important Formulas

Last-two-digit test
N = 100q + r; N is divisible by 4 if and only if r is divisible by 4.

Here, r is the number represented by the last two digits of N. Since 100q is always divisible by 4, only r needs to be checked.

Remainder form
N mod 4 = (last two digits of N) mod 4

The remainder after division by 4 is determined by the last two digits of the number.

Quick Tricks

Check only the last two digits

Ignore all digits except the final two. Test that two-digit number for divisibility by 4.

Example: For 57,824, check 24. Since 24 ÷ 4 = 6, 57,824 is divisible by 4.
Use multiples of 4

The relevant last-two-digit values are multiples of 4, such as 04, 08, 12, 16, 20, 24 and so on up to 96.

Example: In 9,736, the last two digits are 36. Since 36 is a multiple of 4, 9,736 is divisible by 4.

Divisibility Rule of 4 Concepts

Applying the last-two-digit test

To test a number, separate its final two digits and divide that part by 4.

If the final two digits give a remainder of 0, the original number is divisible by 4. If they give any other remainder, the original number is not divisible by 4.

Example: For 4,512, the final two digits are 12. As 12 ÷ 4 = 3, 4,512 is divisible by 4.

Numbers ending in zero

A number ending in 00 is divisible by 4 because 00 represents 0, which is divisible by 4.

For numbers ending in one zero, check the last two digits in the usual way. Thus, 1,240 is divisible by 4 because 40 ÷ 4 = 10, while 1,230 is not divisible by 4 because 30 is not divisible by 4.

Example: 7,500 is divisible by 4 because its last two digits are 00.

Numbers with fewer than two digits

For a one-digit number, test the number itself for divisibility by 4.

Among the non-negative one-digit integers, 0, 4 and 8 are divisible by 4. For a two-digit number, the whole number is the last-two-digit part, so it can be checked directly.

Example: 84 is divisible by 4 because 84 ÷ 4 = 21, whereas 86 is not because it leaves a remainder of 2.

Using the rule to find an unknown digit

When one digit is unknown, choose its value so that the final two digits form a multiple of 4.

Only the last two positions affect divisibility by 4. For a number such as 52x, test 520, 524, 528 and the other possible endings according to the position of x.

Example: For 53x, the possible endings are 30 to 39. The values divisible by 4 are 32 and 36, so x can be 2 or 6.

Divisibility Rule of 4 Video Lessons

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14 Lessons
Lesson 1 of 14 Quick Revision

Divisibility Rules for 2, 4 and 8

Learn how to test whether a number is divisible by 2, 4, or 8 using the relevant digit and last-digit rules, with clear applications for aptitude questions.

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Practice Divisibility Rule of 4 Questions

Practise published questions related to this topic.

184P6 is divisible by 6. Which of the following cannot be the value of P?→ 2The LCM of two numbers 216 and 120 is 1080. Find the HCF of these numbers.→ 3The HCF of two numbers is 8, and their LCM is 240. If the sum of the two numbers is 88, what are the numbers?→ 4What is the HCF of 32, 28, and 24?→ 5What is the Highest Common Factor of 0.48, 0.64 and 0.80?→ 6(√0.0169/1.3) × (0.18/√3.24) × (0.24/√0.0576) = ?→ 7The H.C.F. and L.C.M. of two numbers are 25 and 500, respectively. If the first number is divided by 2, the quotient is 50 and the remainder is zero. Find the second number.→ 8Which of the following numbers is divisible by 49?→ 9Given that √15 = 3.87 and √150 = 12.24, then find the approximate value of √15 + √1500 + √0.015.→ 10B = 700 - A. When B is divided by 3, 4 and 5 the remainder is 1 in each case. What is the value of A?→

Divisibility Rule of 4 Quick Quiz

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Quick Revision Notes

Divisibility Rule of 4: Quick Revision

Use the final two digits to test divisibility by 4.

  • A number is divisible by 4 if its last two digits are divisible by 4.
  • Every multiple of 100 is divisible by 4, so earlier digits do not affect the test.
  • Check endings such as 00, 04, 08, 12, 16, 20, 24 and continuing multiples of 4 up to 96.
  • For a number ending in 00, the number is divisible by 4.
  • For an unknown digit, form the final two-digit number and select values that are multiples of 4.

Divisibility Rule of 4 FAQs

What is the divisibility test for 4?

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, 6,724 is divisible by 4 because 24 is divisible by 4.

Is 1,236 divisible by 4?

Yes. Its last two digits are 36, and 36 ÷ 4 = 9. Therefore, 1,236 is divisible by 4.

Is 2,318 divisible by 4?

No. Its last two digits are 18, and 18 leaves a remainder of 2 when divided by 4.

Why are only the last two digits checked for divisibility by 4?

Any number can be written as 100q + r, where r is its last two-digit part. Since 100q is divisible by 4, divisibility depends only on r.

Which numbers from 1 to 100 are divisible by 4?

They are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96 and 100.

For 53x to be divisible by 4, what can x be?

The final two digits range from 30 to 39. The multiples of 4 in this range are 32 and 36, so x can be 2 or 6.

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