DIVISIBILITY BY 7 AND 8 - RULES WITH EXPLANATION, SOLVED EXAMPLES

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Please study
Multiplication Tables
and
Division before Divisibility By 7 and 8
They are prerequisites here.

Here we study methods that can be used to determine
whether a number is evenly divisible by 7 and 8.

These are shortcuts for testing a number's factors
without resorting to division calculations.

The rules given below transform a given number's divisibility
by a divisor to a smaller number's divisibility by the same divisor.

If the result is not obvious after applying it once,
the rule should be applied again to the smaller number.

We present the rules with examples, in a simple way,
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Divisibility By 7 and 8

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Divisibility Rule for 8

A number is divisible by 8, if the number formed by its last three digits
(hundreds' digit, tens' digit and units' digit) is divisible by 8.

Note : If the number is odd, there is no need to check the rule,
as odd number is not divisible by even number (8).

Example 1 of Divisibility By 7 and 8

Find whether 45567 is divisible by 8 or not.

Solution :
As the number, 45567 is odd, it is not divisible by 8. Ans.

Example 2 of Divisibility By 7 and 8

Find whether 47384 is divisible by 8 or not.

Solution :
We verify whether the number formed by the last three digits (384)
is divisible by 8 or not.


              Dividend
 Divisor   8 )   384   ( 48   Quotient    
                 32
                 ---
                  64
                  64    
                 ---  
                   0   Remainder 
                 ---   

As the remainder is zero, 384 is divisible by 8.
Hence 47384 is divisible by 8. Ans.

Example 3 of Divisibility By 7 and 8

Find whether 289512 is divisible by 8 or not.

Solution :
We verify whether the number formed by the last three digits (512)
is divisible by 8 or not.


              Dividend
 Divisor   8 )   512   ( 64   Quotient    
                 48
                 ---
                  32
                  32    
                 ---  
                   0   Remainder 
                 ---   

As the remainder is zero, 512 is divisible by 8.
Hence 289512 is divisible by 8. Ans.

Example 4 of Divisibility By 7 and 8

Find whether 1756942 is divisible by 8 or not.

Solution :
We verify whether the number formed by the last three digits (942)
is divisible by 8 or not.


              Dividend
 Divisor   8 )   942   ( 117   Quotient    
                 8
                 ---
                 14
                  8    
                ----  
                  62    
                  56
                ----
                   6    Remainder
                ----

As the remainder is not zero, 942 is not divisible by 8.
Hence 1756942 is not divisible by 8. Ans.

Example 5 of Divisibility By 7 and 8

Find whether 19230404 is divisible by 8 or not.

Solution :
We verify whether the number formed by the last three digits (404)
is divisible by 8 or not.


              Dividend
 Divisor   8 )   404   ( 50   Quotient    
                 40
                 ---
                  04
                   0    
                 ---  
                   4   Remainder 
                 ---   

As the remainder is not zero, 404 is not divisible by 8.
Hence 19230404 is not divisible by 8. Ans.

Thus we can check divisible by 8 of any number,
how big it may be, by simply checking the
divisibilty of the number formed by the last three digits.

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