Divisibility

Posted in Terms Defined

Divisibility by 2: If a number has either 0, 2, 4, 6, or 8 in its ones place then it is divisible by 2.

Divisibility by 3: If the sum of the digits of a number is a multiple of 3, then the number is divisible by 3.

Divisibility by 4: A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

Divisibility by 5: If a number has either 0 or 5 in its ones place then it is divisible by 5.

Divisibility by 6: If a number is divisible by 2 and 3 both then it is divisible by 6 also.

Divisibility by 8: A number with 4 digits or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.

Divisibility by 9: If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.

Divisibility by 10: If a number has 0 in the ones place then it is divisible by 10.

Divisibility by 11: Find the difference between the sum of digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11. 

Some more divisibility rules:

  • If a number is divisible by another number then it is divisible by each of the factors of that number.
  • If a number is divisible by two co-prime numbers then it is divisible their product also.
  • If two given numbers are divisible by a number, then their sum is also divisible by that number.
  • If two given numbers are divisible by a number, then their difference is also divisible by that number.