Divisibility Rule of 2: Rules, Tricks and Examples

Divisibility Rule of 2 checks whether an integer can be divided by 2 without a remainder. The test depends only on the last digit of the number. Numbers ending in 0, 2, 4, 6 or 8 are divisible by 2. This page covers the rule, its mathematical basis, shortcuts and solved examples.

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What Is the Divisibility Rule of 2?

A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8. Such numbers are even and leave a remainder of 0 when divided by 2.

The last digit determines divisibility by 2 because every place-value term before the units digit is a multiple of 10, and 10 is divisible by 2. For example, 4,738 ends in 8, so 4,738 is divisible by 2. In fact, 4,738 ÷ 2 = 2,369.

Divisibility Rule of 2 Formula & Tricks

Important Formulas

Last-digit test
N is divisible by 2 if and only if its units digit ∈ {0, 2, 4, 6, 8}.

Read only the units digit. If it is even, the complete integer is divisible by 2.

Place-value form
N = 10q + r, where r ∈ {0,1,2,3,4,5,6,7,8,9}; N is divisible by 2 when r ∈ {0,2,4,6,8}.

The term 10q is always divisible by 2, so the remainder depends on the units digit r.

Quick Tricks

Check only the last digit

Ignore all digits except the units digit. This is the divisibility by 2 trick for both small and very large integers.

Example: In 8,42,716, the last digit is 6, so the number is divisible by 2.
Use the even-number list

A units digit of 0, 2, 4, 6 or 8 gives a positive result; a units digit of 1, 3, 5, 7 or 9 gives a negative result.

Example: 53,284 ends in 4 and is divisible by 2, whereas 53,285 ends in 5 and is not.

Divisibility Rule of 2 Concepts

Why the Units Digit Is Sufficient

Only the units digit can affect the remainder after division by 2.

Write a number as N = 10q + r. Since 10q is divisible by 2, N and r have the same remainder when divided by 2. Therefore, testing r, the units digit, tests the whole number.

Example: For 6,432, write 6,432 = 10 × 643 + 2. The first term is divisible by 2 and the units digit 2 is also divisible by 2, so 6,432 is divisible by 2.

Even and Odd Numbers

Every integer ending in 0, 2, 4, 6 or 8 is even; every integer ending in 1, 3, 5, 7 or 9 is odd.

An even number has the form 2k for an integer k and gives remainder 0 on division by 2. An odd number has the form 2k + 1 and gives remainder 1.

Example: 7,906 is even because 7,906 = 2 × 3,953. The number 7,907 is odd because it is one more than an even number.

Applying the Test to Large Numbers

The number of digits does not affect the divisibility test; only the final digit is checked.

Do not add the digits or divide the entire number to test divisibility by 2. A large integer is divisible by 2 whenever its units digit belongs to the even-digit set.

Example: 98,765,432 ends in 2, so it is divisible by 2.

Numbers Ending in Zero

Every integer ending in 0 is divisible by 2.

A trailing zero represents a multiple of 10, and every multiple of 10 is also a multiple of 2. This includes 0 itself because 0 = 2 × 0.

Example: 12,340 ÷ 2 = 6,170, so 12,340 is divisible by 2.

Divisibility Rule of 2 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 2 Questions

Practise published questions related to this topic.

1What is the Highest Common Factor of 0.42, 0.60 and 0.78?→ 2What is the least number, which when divided by 8, 14, 15 and 20 leaves remainder 5 in each case?→ 3If the ratio of two numbers is 3 : 8, and their HCF is 6, then their LCM is:→ 4The LCM of two numbers is 168, and their HCF is 14. If one of the numbers is 42, find the other number.→ 5If √x = 0.12, then the value of x + √x is:→ 6The sum of square of two consecutive natural numbers is 313. What is the larger of the two numbers?→ 7What is the square root of 1444?→ 8What is the smallest natural number that should be added to 9054 such that a remainder of 6 is left when the resulting number is divided by each of the numbers 28, 24, 56 and 29?→ 9The sum of a number and its positive square root is 30. What is the value of the number?→ 10Simplify √(1624+√(3225+√(419+157))) .→

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Quick Revision Notes

Divisibility Rule of 2: Quick Revision

Use the units digit to test divisibility by 2.

  • The units digit must be 0, 2, 4, 6 or 8.
  • A number divisible by 2 is an even number.
  • Units digits 1, 3, 5, 7 and 9 indicate that the number is not divisible by 2.
  • The other place-value terms are multiples of 10 and therefore do not affect divisibility by 2.
  • The rule applies to integers, including 0 and negative integers.

Divisibility Rule of 2 FAQs

What is the divisibility test for 2?

Check the last digit. If it is 0, 2, 4, 6 or 8, the number is divisible by 2.

Is 45,678 divisible by 2?

Yes. Its last digit is 8, so 45,678 is divisible by 2. The quotient is 22,839.

Is a number ending in 5 divisible by 2?

No. Numbers ending in 5 are odd and leave a remainder of 1 when divided by 2.

Do we need to add the digits to test divisibility by 2?

No. Digit addition is not required. Only the units digit is checked for divisibility by 2.

Is 0 divisible by 2?

Yes. 0 is divisible by 2 because 0 = 2 × 0, and its last digit is 0.

Are all numbers divisible by 2 also divisible by 4?

No. Divisibility by 2 only requires an even last digit. For example, 14 is divisible by 2 but not by 4.

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