Divisibility test

 Tests for Divisibility

Divisibility Tests	Example
A number is divisible by 2  if the last digit is 0, 2, 4, 6 or 8.	178 is divisible by 2 since the last digit is 8.
A number is divisible by 3  if the sum of the digits is divisible by 3.	138 is divisible by 3 since the sum of the digits is 15 (1+3+8=12), and 12 is divisible by 3.
A number is divisible by 4  if the number formed by the last two digits is divisible by 4.	312 is divisible by 4 since 12 is divisible by 4.
A number is divisible by 5  if the last digit is either 0 or 5.	295 is divisible by 5 since the last digit is 5.
A number is divisible by 6  if it is divisible by 2 and it is divisible by 3.	168 is divisible by 6 since it is divisible by 2  and it is divisible by 3.
A number is divisible by 8  if the number formed by the last three digits is divisible by 8.	8,120 is divisible by 8 since 120 is divisible by 8.
A number is divisible by 9  if the sum of the digits is divisible by 9.	540 is divisible by 9 since the sum of the digits is 18 (5+4+0=9), and 9 is divisible by 9.
A number is divisible by 10  if the last digit is 0.	1,370 is divisible by 10 since the last digit is 0.

Examples.

Example 1:	Determine whether 150 is divisible by 2, 3, 4, 5, 6, 9 and 10.
	150 is divisible by 2 since the last digit is 0.
	150 is divisible by 3 since the sum of the digits is 6 (1+5+0 = 6), and 6 is divisible by 3.
	150 is not divisible by 4 since 50 is not divisible by 4.
	150 is divisible by 5 since the last digit is 0.
	150 is divisible by 6 since it is divisible by 2 AND by 3.
	150 is not divisible by 9 since the sum of the digits is 6, and 6 is not divisible by 9.
	150 is divisible by 10 since the last digit is 0.

Example 2:	Determine whether 225 is divisible by 2, 3, 4, 5, 6, 9 and 10.
	225 is not divisible by 2 since the last digit is not 0, 2, 4, 6 or 8.
	225 is divisible by 3 since the sum of the digits is 9, and 9 is divisible by 3.
	225 is not divisible by 4 since 25 is not divisible by 4.
	225 is divisible by 5 since the last digit is 5.
	225 is not divisible by 6 since it is not divisible by both 2 and 3.
	225 is divisible by 9 since the sum of the digits is 9, and 9 is divisible by 9.
	225 is not divisible by 10 since the last digit is not 0.

Example 3:	Determine whether 7,168 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.
	7,168 is divisible by 2 since the last digit is 8.
	7,168 is not divisible by 3 since the sum of the digits is 22, and 22 is not divisible by 3.
	7,168 is divisible by 4 since 168 is divisible by 4.
	7,168 is not divisible by 5 since the last digit is not 0 or 5.
	7,168 is not divisible by 6 since it is not divisible by both 2 and 3.
	7,168 is divisible by 8 since the last 3 digits are 168, and 168 is divisible by 8.
	7,168 is not divisible by 9 since the sum of the digits is 22, and 22 is not divisible by 9.
	7,168 is not divisible by 10 since the last digit is not 0 or 5.

Example 4:	Determine whether 35,120 is divisible by 2, 3, 4, 5, 6, 8, 9 and 10.
	35,120 is divisible by 2 since the last digit is 0.
	35,120 is not divisible by 3 since the sum of the digits is 11, and 11 is not divisible by 3.
	35,120 is divisible by 4 since 20 is divisible by 4.
	35,120 is divisible by 5 since the last digit is 0.
	35,120 is not divisible by 6 since it is not divisible by both 2 and 3.
	35,120 is divisible by 8 since the last 3 digits are 120, and 120 is divisible by 8.
	35,120 is not divisible by 9 since the sum of the digits is 11, and 11 is not divisible by 9.
	35,120 is divisible by 10 since the last digit is 0. Divisibility by 11     A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.(This abstract and confusing sounding rule is much clearer with a few examples)  Use the divisibility calculator below to determine if any number is divisible by eleven. Type in any number that you want, and the calculator will explain whether or not it's divisible by 11 based on this rule.

A number is divisible by 13 if the following is true:

• Multiply the ones digit by 4.
• Add this value from the rest of the number.
• Continue this pattern until you find a number you know is or is not divisible by 13.

Example        3159 is divisible by 13 because

a) 9 x 4 = 36.

b) 315  + 3 6 = 351 
c) 1 x 4  = 4
d)  35 + 4 = 39  which is divisible by 13.

Example        22113 is divisible by 13 because

a) 3 x 4 = 12.

b) 2211  +12  =   2223 
c) 3 x 4  = 12
d)  222 + 12 = 234
e) 4x 4 = 16
f)  23 + 16 = 39   which is divisible by 13.