DIVISIBILITY RULE FOR 7

In a number, if the difference between twice the digit in one's place and the number formed by other digits is either zero or a multiple of 7, then the number is divisible by 7. 

Example 1 :

Check whether 91 is divisible by 7. 

Solution :

In the given number 91, twice the digit in one's place is

=  2 ⋅ 1

=  2

The number formed by the digits except the digit in one's place is

=  9  

The difference between twice the digit in one's place and the number formed by the other digits is 

=  9 - 2

=  7

7 is divisible by 7.

So, the given number 91 is divisible by 7.

Example 2 :

Check whether 504 is divisible by 7. 

Solution :

In the given number 504, twice the digit in one's place is

=  2 ⋅ 4

=  8

The number formed by the digits except the digit in one's place is

=  50

The difference between twice the digit in one's place and the number formed by the other digits is 

=  50 - 8

=  42

42 is divisible by 7.

So, the given number 504 is divisible by 7.

Example 3 :

Check whether 783 is divisible by 7. 

Solution :

In the given number 783, twice the digit in one's place is

=  2 ⋅ 3

=  6

The number formed by the digits except the digit in one's place is

=  78

The difference between twice the digit in one's place and the number formed by the other digits is 

=  78 - 6

=  72

72 is not divisible by 7.

So, the given number 783 is not divisible by 7.

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