Divisibility by 20
- If the number formed by the two digits at the tens place and unit place in order is divisible by 20 then the number is divisible by 20 else not.
- If ten times the digit at the tens place when added to the digit at the unit place is divisible by 20 then the number is divisible by 20 else not. The digit at the unit place must be zero.
Proof:
Let the number be abcd.
abcd can be written as
a×1000 + b×100 + c×10 + d
which can also be written as
a×20×50 + b×20×5 + c×10 + d
Every power of 10 i.e. 10^{x} is divisible by 20 if x>1.
So a×20×50 + b×20×5 is divisible by 20 as it has 20 as factor or common factor.
The number is divisible by 20 if cd is divisible by 20.
The digits left is c×10+d
d can not be other than 0, the digit at tens place can be 0,2,4,6 and 8.
The above is divisible by 20 if 10c+d is divisible by 20.
Remainder
- The remainder of the number formed by the last two digits when divided by 20 is the remainder of the original number.
- If the number formed by the last two digits is ab. Then the remainder is the remainder of the number 10a+b, when divided by 20.
Examples
- Is 348 divisible by 20.
The number formed by the last two digits is 48. 48 is not divisible by 20 it is greater by 8 therefore the number is not divisible by 20. Remainder is 8.
- Is 3480 divisible by 20.
The number formed by the last two digits is 80. 80 is divisible by 20 therefore the number is divisible by 20.