# Divisible by 8

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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