Weite divisibility fost of 10,5,2,3 and!
Answers
Divisibility rule by 10:
If the unit digit of the number is 0, then the number is divisible by 10.
Proof:
Take a number abc,
abc can be written as 100a + 10b + c
100 divisible by 10, so, 100a is also divisible by 10.
10 divisible by 10, so, 10a is also divisible by 10. The only digit left is "c", the number can only be is divisible by 10 if and only if c = 0
Divisibility rule by 5:
If the unit digit of a number is 5 or 0, then the number is divisible by 5.
Proof:
Take a number abc
abc can be written as 100a + 10b + c
100 and 10 are divisible by 5, so 100a and 10b are also divisible by 5. so the number is divisible by 5 if "c" is divisible by 5. Which is possible when c is 5 or 0
Divisibility rule by 2:
If the unit digit of a number is even, then the number is divisible by 2
Proof:
Take a number abc
abc can be written as 100a + 10b + c
100 and 10 are divisible by 2, so 100a and 10b are also divisible by 2. so the number is divisible by 2 if "c" is divisible by 2. Which is possible when c is even.
Divisibility rule by 3:
if the sum of the digits of the number is divisible by 3, then the number is divisible by 3.
Proof:
Take a number abc
abc can be written as 100a + 10b + c
=> 99a + a + 9b + c
99a and 9b are divisible by 3, So, the number is divisible by 3 if ( a + b + c) is divisible by 3.
Note: We've performed it with 3 digit number, but it is applicable for numbers with any number of digits.