Intermediate Test Prep (Grades7-8) Divisibility Rules

There are several methods for testing the divisibility of a number without actually performing the division.

A Number can be divisible by...

2	If the last digit is even.
3	If the sum of the digits can be divided by 3.
4	If the last two digits can be divided by 4.
5	If the last digit is 5 or 0.
6	If the number can be divided by 2 and 3.
8	If the last three digits can be divided by 8.
9	If the sum of the digits can be divided by 9.
10	If the last digit is 0.

Example 1

Which whole numbers from 1 to 10 are divisors of 9060?

Solution

(Remember that a divisor is a factor.)

	The number 1 is a factor of any number
	Since 9060 is an even number it is divisible by 2
	The sum of the digits is 15 so 9060 is divisible by 3 but not by 9
	The last two digits are 60 and 60 is divisible by 4
	The number ends with a 0 so it is divisible by 5 and 10
	Since 9060 is divisible by 2 and 3, 6 must also be a factor
	We must divide 9060 by 7 to see if it is a factor, it is not
	The last three digits, 060 or 60, is not divisible by 8

The numbers 1, 2, 3, 4, 5, 6, and 10 are divisors of 9060.

Example 2

List the single digit divisors of 1356.

Solution

(Single digits only include 1-9.)

	The number 1 is a factor of any number
	1356 is even so 2 is a factor
	The sum of the digits is 15 so 1356 is divisible by 3 but not by 9
	The last two digits, 56, is divisible by 4
	Since the last number is a 6 neither 5 nor 10 are factors
	1356 is divisible by 6 because 2 and 3 are factors
	We must divide 1356 to see if 7 is a factor, it is not
	The last three digits, 356, is not divisible by 8

The single-digit divisors of 1356 are 1, 2, 3, 4, and 6.