Divisibility Rules

Divisibility Rules

Introduction

There are several divisibly rules to know. So we can divide numbers easily.

Divisibility rules

2 divisibility rule– Any number that has its units place as 2,4,6,8 or 0 that means the number is divisible by 2.

Example:

3256, 08, 190, 122

 

3 divisibility rule–If the sum of the number is a multiple of 3 or divisible by 3 then the whole number is divisible by 3.

Example:

3570  -> 3+5+7+0 = 15  -> 15 is multiple of 3 so 3570  is divisible by 3.

 

4 divisibility rule– If the last two numbers are divisible by 4 then the whole number is divisible by 4.

Example:

136, 134528, 14324508 -> last two digits of these number are divisible by 4, so all numbers are divisible by 4.

 

5 divisibility rule-If the units place is a 1 or 0 then it is divisible by 5.

Example:

50, 45670,55

 

6 divisibility rule-If the number is divisible by both 2 & 3 then it is divisible by 6.

Example:

12324,3570,6321.

 

7 divisibility rule- Double the units place (x 2) then subtract the product by the rest of the numbers, then if the difference is 0 or divisible by 7. continue the same process until you get the divisibility of 7 or 0.  Then the whole number is divisible by 7.

Example:
1. 455→5×2=10 →45-10=35 and 35 is multiple of 7 so 455 is divisible by 7.

2.   9681→1×2=2→968-2=986
966→6×2=12→96-12=84
84→4×2=8→8-8=0

so 9681 is divisible by 7.

and 35 is multiple of 7 so 455 is divisible by 7.

 

8 divisibility rule–if the last three digits are divisible by 8 then whole digit is divisible by eight

Example:
12104→104÷8= remainder 0 so 12104 is divisible by eight.

 

9 divisibility rule-If the sum of the number is a multiple of 9 or divisible by 9 then the whole number is divisible by 9.

Example:

88 is divisible because 8+8=18 and18 divisible by nine.

 

10 divisibility rule–If the units place is 0 then it is divisible by 10

Example:

10,100,1890.

 

11 divisibility rules-Find the sum of odd places and even places and subtract the sums and if the difference is divisible by 11 or 0 then the number is divisible by 11.

Example:

odd places-in bold letters
even places= normal text
29601

2+6+1=9
9+0=9
9-9=0
so 29601 is divisible by 11