Divisibility Rule of 8: Rules, Tricks and Examples

Divisibility Rule of 8 determines whether a number can be divided by 8 without leaving a remainder. For numbers with three or more digits, check only the last three digits. This page explains the divisibility by 8 rule, its mathematical basis, quick calculation methods and solved examples.

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What Is the Divisibility Rule of 8?

A number is divisible by 8 if its last three digits form a number divisible by 8. For a number having fewer than three digits, test the complete number.

This rule works because 1000 is divisible by 8. If a number is written as N = 1000q + r, where r is its last three-digit part, then N and r have the same remainder when divided by 8. Therefore, 5,216 is divisible by 8 because its last three digits, 216, are divisible by 8: 216 ÷ 8 = 27.

Divisibility Rule of 8 Formula & Tricks

Important Formulas

Remainder form
N = 1000q + r, so N mod 8 = r mod 8

Here, r represents the last three digits of N. Since 1000 mod 8 = 0, only r determines divisibility by 8.

Divisibility condition
N is divisible by 8 if and only if the last three digits are divisible by 8

The last three-digit part may include leading zeroes, such as 016 or 008.

Quick Tricks

Check only the last three digits

Ignore all digits before the last three digits. Divide the remaining three-digit number by 8 or compare it with a nearby multiple of 8.

Example: For 47,832, check 832. Since 832 ÷ 8 = 104, 47,832 is divisible by 8.
Use the nearest multiple of 8

If direct division is inconvenient, find whether the last three digits equal 8 times an integer.

Example: For 6,574, the last three digits are 574. Since 8 × 71 = 568 and 8 × 72 = 576, 574 is not divisible by 8.

Divisibility Rule of 8 Concepts

Testing a Three-Digit or Larger Number

For a number with at least three digits, divide only its last three digits by 8.

The digits before the final three do not affect divisibility because every multiple of 1000 is also a multiple of 8. Thus, for 12,344, test 344 rather than the complete number. Since 344 ÷ 8 = 43, 12,344 is divisible by 8.

Example: 91,216 is divisible by 8 because 216 ÷ 8 = 27.

Testing Numbers with Fewer Than Three Digits

For a one- or two-digit number, test the entire number because it is already the complete final part.

The two-digit multiples of 8 include 16, 24, 32, 40, 48, 56, 64, 72, 80 and 88. Therefore, 72 is divisible by 8, while 74 is not because 74 ÷ 8 leaves a remainder of 2.

Example: For 96, 96 ÷ 8 = 12, so 96 is divisible by 8.

Using Leading Zeroes in the Last Three Digits

A last part with fewer than three visible digits can be written with leading zeroes before applying the rule.

For example, the last three digits of 7,016 are 016, which has the same value as 16. Since 16 is divisible by 8, 7,016 is divisible by 8. Similarly, 9,008 is divisible by 8 because 008 equals 8.

Example: For 3,204, the final part is 204, and 204 ÷ 8 = 25.5; therefore, 3,204 is not divisible by 8.

Finding the Remainder When Dividing by 8

The remainder of a number on division by 8 is the same as the remainder obtained from its last three digits.

Write N = 1000q + r. Since 1000q is divisible by 8, the remainder of N depends only on r. For 4,219, the last three digits are 219; 219 = 8 × 27 + 3, so the remainder is 3.

Example: The remainder when 18,219 is divided by 8 is 3 because 219 leaves remainder 3.

Divisibility Rule of 8 Video Lessons

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14 Lessons
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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 8 Questions

Practise published questions related to this topic.

1How many numbers among 1210, 1331, 1442, 1553 are divisible by 11?→ 2A data analyst is studying a series of zoomed-in satellite resolutions. The base square root reference she uses is: √18225 = 135 She now wants to quickly compute the total of square roots for four scaled-down values (by factors of 10): (√182.25 + √1.8225 + √0.018225 + √0.00018225) What is the value of this sum?→ 3The L.C.M. of two numbers is 210 and their H.C.F. is 3. If the first number is divided by 3, the quotient is 7 and the remainder is 0. The second number is:→ 4√((0.064 × 0.256)/(0.004 × 0.16)) = ?→ 5√18.49 + √0.1849 + √0.001849 + √0.00001849 = ?→ 6What is the smallest number which when increased by 30 is exactly divisible by 6, 10 and 12?→ 7Two numbers have HCF 12, LCM 480, and their sum is 156. Find the numbers.→ 8If the 8-digit number 79243p25 is divisible by 11, then the minimum value of p is:→ 9What is the largest 2 digit number which is exactly divisible by both 8 and 7?→ 10What is the smallest natural number that should be added to 5023, such that a remainder of 5 is left when the resulting number is divided by each of the numbers 20, 98, 35 and 21?→

Divisibility Rule of 8 Quick Quiz

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Quick Revision Notes

Divisibility Rule of 8: Quick Revision

Use the final three digits to test divisibility by 8.

  • A number is divisible by 8 when its last three digits are divisible by 8.
  • For numbers with fewer than three digits, test the complete number.
  • The rule follows from 1000 = 8 × 125.
  • Leading zeroes may be added to make the final part three digits, such as 16 becoming 016.
  • For N = 1000q + r, N and r have the same remainder when divided by 8.
  • If the last three digits leave a non-zero remainder on division by 8, the complete number is not divisible by 8.

Divisibility Rule of 8 FAQs

What is the divisibility test for 8?

A number is divisible by 8 if its last three digits form a number divisible by 8. If the number has fewer than three digits, test the whole number.

Why are only the last three digits checked for divisibility by 8?

Because 1000 = 8 × 125, every place-value part before the last three digits is divisible by 8. Hence, only the final three-digit part affects the remainder.

Is 12,016 divisible by 8?

Yes. Its last three digits are 016, which equals 16, and 16 ÷ 8 = 2.

Is 5,734 divisible by 8?

No. Its last three digits are 734. Since 8 × 91 = 728 and 8 × 92 = 736, 734 is not divisible by 8.

What is the remainder when 27,451 is divided by 8?

Check 451. Since 451 = 8 × 56 + 3, the remainder is 3.

Are numbers ending in 000 always divisible by 8?

Yes, provided the number is an integer. Its last three digits are 000, and 0 is divisible by 8; for example, 14,000 ÷ 8 = 1,750.

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