NUMBERS AND DIVISIBILITY

DIVISIBILITY TEST OF NATURAL NUMBERS

DIVISIBILITY BY 2:

A number is divisible by two if its  last digit is divisible by 2 i.e. if its last digit is  even i.e. 0, 2, 4, 6 or 8

For example 100, 144, 186, 198 and 10004 are divisible by 2

DIVISIBILITY BY 3:

A number is divisible by 3 if the sum of its digits is divisible by three  

For example 300 is divisible by three because the sum of the digits  3 + 0 + 0 = 3 is divisible by 3

207 is divisible by three because  the sum of the digits 2 + 0 + 7 = 9   is divisible by 3.

DIVISIBILITY BY 4:

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

For example  4548 is divisible by 4 because the last two digit, 4 and 8 sum up to  a multiple of 4 i.e. 4 + 8 = 12 which is a multiple of 4.

DIVISIBILITY BY 5:

A number is divisible by 5 if the last digit is 0 or 5.

For example 190, 35, 95, 1005 .etc…. are all divisible by 5 because ther last digit is either 0 or 5.

DIVISIBILITY BY 6:

A number is divisible by 6 if it is divisible b both 2 and 3.

For example 36 is divisible by both 2 and 3. So, it is divisible by 6.

DIVISIBILITY BY  8:

A number is divisible by 8 if the number formed by the last three digits is divisible by 8.

For example 1056 is divisible by 8 because  056 is divisible by 8.

 

DIVISIBILITY BY 9:

A number is divisible by 9 if the sum of its digits is divisible by 9.

For example 18 is divisible by 9 because 1 + 8 = 9 is divisible by 9.

261261 is divisible by 9 because 2 + 6 + 1 +2 + 6 + 1=18 is divisible by 9

DIVISIBILITY BY 10:

A number is divisible by 10 if its last digit is 0.

For example  290, 710, 3480, 200 are all divisible by 10.