Divisibility rules can simplify complex calculations and problem-solving. This guide describes the specific rule for divisibility by 8, providing clear explanations and practical examples.
Divisibility Rule of 8 states that a number is divisible by 8 if the last three digits of the number form a number that is divisible by 8. This rule simplifies the process of determining whether larger numbers can be evenly divided by 8.
For Example: Check if 5128 is divisible by 8.
The last three digits are 128.
128 ÷ 8 = 16 (which is a whole number)
Since 128 is divisible by 8, 5128 is divisible by 8.
This article explains the divisibility by 8 rule provides examples, and offers practice problems to help you understand and apply it effectively.
The flow chart showing the divisibility rule of 8:
More Examples of Divisibility Rule of 8
3896 : The last three digits of 3,896 are 896.
896 ÷ 8 = 112, with no remainder.
Therefore, 3,896 is divisible by 8.
23419 : The last three digits of 23419 are 419.
419 ÷ 8 = 52.375 which is not a whole number.
Therefore, 23419 is not divisible by 8.
Proof of Divisibility Rule of 8
N = 10n an + 10n-1 an-1 + 10n-2 an-2 + ..... + 102 a2 + 10 a1 + a0
Taking mod 8 of N, we get
N ≡ 0 + 0 + 0 + ⋯ + 102 a2 + 10 a1 + a0 (mod 8) (as 10k, where k ≥ 3, is always divisible by 8)
≡ 100a2 + 10a1 + a0 (mod 8)
Therefore, N ≡ 0 (mod 8) if 100a2 + 10a1 + a0 =
Thus, if the hundreds, tens, and units places of a number taken in that order are divisible by 8, then the number is also divisible by 8.
Divisibility Test of 8 for Large Numbers
Divisibility rules are various rules that are used for making division easy and quick. Smaller numbers can be easily check for divisibility of 8 but for larger numbers divisibility rules are used to check whether they are divisible by 8 or not.
Divisibility rule of 8 states that for very large number check if the last three digits of the number are either 000 or divisible by 8 then the whole number is divisible by 8.
Also, Check:
Divisibility Rule of 8 Solved Questions
Example 1: Check divisible by 8 for 172896.
Solution:
Given number 172896
To check its divisibility by 8 without performing division operations we checked whether its last three digits are divisible by 3 or not
We can see the last three digits of 172896 are 896
Since,
896/8 = 112 with no remainder
We can say that 172896 is divisible by 8
Example 2: Check 262899 is divisible by 8 or not.
Solution:
Given number 262899
To check its divisibility by 8 without performing division operations we checked whether its last three digits are divisible by 3 or not
We can see the last three digits of 262899 are 899
Since,
899/8 = 112.375 (with remainder)
We can say that 262899 is not divisible by 8
Example 3: Check 5126 is divisible by 8 or not.
Solution:
Given number 5216
To check its divisibility by 8 without performing division operations we checked whether its last three digits are divisible by 3 or not
We can see the last three digits of 5216 are 216
Since,
216/8 = 27 with no remainder
We can say that 5126 is divisible by 8
Example 4: Check 9304 is divisible by 8 or not.
Solution:
Given number 9304
To check its divisibility by 8 without performing division operations we checked whether its last three digits are divisible by 3 or not
We can see the last three digits of 9304 are 304
Since,
304/8 = 38 with no remainder
We can say that 9304 is divisible by 8
Divisibility Rule of 8 Worksheet
Try these problems to practice checking divisibility by 8:
1. Is 745128 divisible by 8?
2. Is 930475 divisible by 8?
3. Is 123008 divisible by 8?
4. Is 102400 divisible by 8?
5. Is 123456 divisible by 8?
6. Determine whether 7852 is divisible by 8.
7. Check if the number 9340 is divisible by 8.
8. Is the number 5600 divisible by 8?
Also Check: Practice Questions on Divisibility Rules