Divisibility Rules

A Divisibility Rules is a shortcut method of discovering whether a given number is divisible by a certain divisor without performing the division, usually by examining its digits. Although there are divisibility rules for numbers in any base, and they are all different, this section presents rules.


Divisibility Rules of some numbers are given below:

A Number is divisible by:
If
Example
2
 Its unit's digit is 0,2,4,6 or 8. 36 is divisible but not 39.
3
 The sum of its digit is divisible by 3. 144 (1+ 4 + 4 = 9 ÷3 = 3) yes
4
The number formed by its digit in ten's and unit's place is divisble by 4. 348 (48 ÷ 4 =12) yes
5
Its unit's digit is 0 or 5. 450 , 855 is divisible but not 806.
6
 It is divisible by both 2 and 3. 114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = which is not a whole number) No
7
 If you double the last digit and subtract it from the rest of the number and the answer is: 1) 0, or 2) divisible by 7 (Note: you can apply this rule to that answer again if you want) 672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=not a whole number) No
8
 A number is divisible by 8.if the number formed by its digits in hundred's,ten's and units places are divisible by 8 109816 (816÷8=102) Yes
216302 (302÷8 = not a whole number) No
9
 A number is divisible by 9,if the sum of its digits is divisible by 9 1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10
 A number is divisible by 10 if its unit's place digits is zero 240 is
221 is not
11
A number is divisible by 11,if the difference of the sum of its digits in odd places and the sum of its digits in even places is eiether 0 or multiple of 11 1364 ((3+4) - (1+6) = 0) Yes 3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
12
 A number is divisible by 12 if it is divisible by 4 & 3 648 (6+4+8=18 and 18÷3=6, also 48÷4=12) Yes
916 (9+1+6=16, 16÷3= 5 1/3) No
15
 A number is divisible by 15 if it is divisible by 3 and 5 both 465 is divisible by 3 and 5 both so with 15 yes otherwise No.
16
A number is divisible by 16 if the number formed by the last 4 digits is divisible by 16 25,8000 ( 8000÷ 16 = 500) yes
18
A number is divisible by if it is divisible by 2 & 9 both 450( 4+5+0= 9 ÷ 9) yes
450 ÷ 2 =225 yes
450 is divisible by 18
20
A number is divisible by 20 if its units digit is 0 and its tens digit is even 780 ( unit digit 0 and tens digit is 8 even number) yes
22
 A number is divisible by 22 if it is divisible by 2 & 11 4466 ( (4+6) -(4+6))= 0 yes by 11
and 4466 ÷ 2 =406 so yes by 22
25
 A number is divisible by 25 if the number formed by the last two digits is any of 0,25,50 or 75 1225 ( last two digits are 25) yes

Factors and Multiples

• Prime and Composite Numbers
• Divisibility rules
• Prime Factorization
• H.C.F or G.C.F
• L.C.M
• Application on LCM

From Divisibility rules to Factors and Multiples

Number System

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