The most common method to check whether a number is divisible by 8 is to divide and see if the quotient is a whole number or not? If the quotient is a whole number then the given number is divisible by 8. But there is an easier way to check by using the divisibility rule.
Divisibility Rule of 8: The divisibility rule of 8 states that if the number formed by taking the last three digits is divisible by 8 then the whole number is divisible by 8.
For Example: Check whether 5864 is divisible by 8 or not?
Since the last three digits are 864 and 864/8 = 108. Hence, the number 5864 is divisible by 8.
Here are few Examples on the Divisibility Rule of 8:
1. Check whether the following number are divisible by 8 or not?
(i) 7655
(ii)3248
(iii) 8880
(iv) 3697
(v)1154
(vi)7256
(vii) 4566
(viii)1008
(ix) 2726
(x) 9635
Solution:
(i) 7655
The last three digits = 655
Now 655 is not divisible by 8 as it gives = 81.875. Hence, 7655 is not divisible by 8
(ii)3248
The last three digits = 248
Now 248/8 = 31. Hence, 3248 is divisible by 8
(iii) 8880
880 is the last three digits
880/8 = 110. Hence 8880 is divisible by 8
iv) 3697
The last three digits = 697
Now 697 divided by 8 is 87.125. Hence, 3697 is not divisible by 8
v)1154
154 is formed by the last three digits
154/8 = 19.25 (which is not a whole number). Hence, 1154 is not divisible by 8
(vi)7256
The last three digits = 256
Now 256/8 = 32. Hence, 7256 is divisible by 8
(vii) 4566
The last three digits = 566
Now, 566 divided by 8 = 70.75 (not a whole number). Hence, 4566 is not divisible by 8
(viii)1008
008 is the last three digit
Now, 8/8 = 1. Hence, 1008 is divisible by 8
(ix) 2726
The last three digit = 726
Now, 726 divided by 8 = 90.75. Hence, 2726 is not divisible by 8
(x) 9635
The last three digits = 635
635 divided by 8 is 79.375
As, 635 is not divisible by 8 so, 9635 is also not divisible by 8
2. Rewrite the series with the numbers that are divisible by 8 with a different color:
8484 4295 6264 1020 3024 7728 5656 7432 5040 5689 4433 1223
Solution:
8484 4295 6264 1020 7432 5040 5689 3024 4433 5656 1223 7728
3. Fill in the blanks with digits o as to make the following number divisible by 8:
(i) 32 … 8
(ii) 10 … 2
(iii) 2 … 48
(iv) 564 …
(v) 410 …
(vi) 874 …
(vii) 30…6
(viii) 4 …16
Solution:
(i) 3288
(ii) 1032
(iii) 2848
(iv) 5640
(v) 4104
vi) 8744
(vii) 3016
(viii) 4816
Note: In the above example we have to put such digits so that the number formed by the last three digit is divisible by 8.
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