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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