How to know whether a given number, however large is divisible by 2, divisible by 3,4,5,6 and 10 .There are fixed divisibility test and divisibility rules for checking the divisibility of any given numbers. For different numbers there are different rules to divide with . So in this post we are going to discuss these divisibility rules with examples one by one. Although there are divisibility test for fraction also ,but this post will be restricted to natural numbers.
Divisibility rules for 2
To check whether the given number, however large is divisible by 2 ,we have to check its right most digit/Unit place digit, if it is even number or zero.Then the given number is definitely divisible by 2
For Example
12 is divisible by 2 as its right most digit is 2 which is Even .
3548 is divisible by 2 as its right most digit is 8 which is Even
999998 is divisible by 2 as its right most digit is 8 which is Even .
65989564 is divisible by 2 as its right most digit is 4 which is Even.
22222229 is not divisible by 2 as its right most digit is 9 which is not A Even number.
589423100780 is divisible by 2 as its right most digit is 0 .
357913579571536 is divisible by 2 as its right most digit is 6 which is Even although all the remaining digits are odd.
Divisibility rules for 3
To check whether the given number, however large is divisible by 3,we have to check the SUM of all its digits, if its sum is divisible by 3 then the given number is divisible by 3, If sum of all the digits of given number is again a large number then add the result so obtained and apply the rule again which is said earlier.
For Example
15 is divisible by 3 as sum of all its digits 1 + 5 = 6 is divisible by 3 .
2678 is not divisible by 3 as sum of all its digits 2 + 6 + 7 + 8 = 23 = 3 + 3 = 5 is not divisible by3 .
98784552 is not divisible by 3 as sum of all its digits 9 + 8+ 7+ 8+ 4 + 5 + 5 + 2 = 48 = 4 + 8 = 12 = 1 + 2 = 3 is not divisible by 3.
359875269 is divisible by 3 as sum of all its digits 3 + 5 + 9 +8 +7 + 5 + 2 + 6 + 9 = 54 = 5 + 4 = 9 is divisible by 3.
3597841137 is divisible by 3 as sum of all its digits 3 + 5 + 9 + 7 + 8 + 4 + 1 + 1 + 3 + 7 = 48 = 12 is divisible by 3 .
Divisibility rules for 4
If the last two digits of a number is divisible by 4 ,Then the number is divisible by 4 . The number having two or more zeros at the end is also divisible by 4.
For Example
134826900 : As ther are two zeros at the end,so the given number is divisible by 4.
13444255452 : As the last two digits number (52) is divisible by 4 ,the given number is divisible by 4.
35888875698549 : As the last two digits number (49) is not divisible by 4 ,the given number is not divisible by 4
97971349999567776 : As the last two digits number (76) is divisible by 4 ,the given number is divisible by 4.
44444444444444444449 : As the last two digits number (49) is not divisible by 4 ,the given number is not divisible by 4.
Divisibility rules for 5
To check whether the given number, however large is divisible by 5 ,we have to check its right most digit/Unit place digit,if it is 5 or zero. Then the given number is definitely divisible by 5.I.e if the given number ends with 0 or 5 then it is divisible by by 5.
For Example
35 is divisible by 5 as its right most digit is 5.
97835 is divisible by 5 as its right most digit is 5.
6854940 is divisible by 5 as its right most digit is 0.
35000000355 is divisible by 5 as its right most digit is 5.
3579515465855 is divisible by 5 as its right most digit is 5.
12345678888880 is divisible by 5 as its right most digit is 0.
568954975311525 is divisible by 5 as its right most digit is 5.
55555555555556 is not divisible by 5 as its right most digit is 6.
66666666666666665 is divisible by 5 as its right most digit is 5.
568954975311525 is divisible by 5 as its right most digit is 5.
55555555555556 is not divisible by 5 as its right most digit is 6.
66666666666666665 is divisible by 5 as its right most digit is 5.
Divisibility rule for 6
For any number to be divisible by 6 ,it must be divisible by both 2 and 3 ,then the given number is divisible by 6, Therefore
1) The number should ends up with an even digits or zero and
2) The sum of its digit should be divisible by 3.
For Example :
56898 is divisible by 6 as sum of its digits is 5 + 6 + 8 + 9 + 8 = 36 = 3 + 6 = 9 so it is divisible by 3 and last digit is even ,as the given number is divisible by both 2 and 3 ,so it is divisible by 6.
3578952 As the last digit is even so the given number is divisible by 2 and sum of all its digits is 3 + 5 +7 + 8 + 9 + 5 + 2 = 39 = 4 + 2 = 6 which is also divisible by 3 ,which implies the given number is divisible by both 2 and 3. Therefore the given number is divisible by 6 as well.
25689879798 is divisible by 6 as sum of its digits is 2 + 5+ 6 + 8 + 9 + 8 + 7 + 9 + 7 + 9 + 8 =78 = 15 = 1 + 5 = 6 so it is divisible by 3 and last digit is even ,as the given number is divisible by both 2 and 3 ,so it is divisible by 6.
35658999962 is not divisible by 6 as sum of its digits is 3 + 5 + 6 + 5 + 8 + 9 + 9 + 9 + 9 + 6 + 2 = 71 = 7 + 1 = 8 so it is not divisible by 3 and last digit is not even ,so it is not divisible by 6.
35789248956 As the last digit is even so the given number is divisible by 2 and sum of all its digits is 3 + 5 + 7+ 8+ 9+ 2+ 4 + 8+ 9 + 5 + 6 = 66 = 6 + 6 = 12 = 1 + 2 = 3 which is also divisible by 3 ,which implies the given number is divisible by both 2 and 3. Therefore the given number is divisible by 6 as well.
Divisibility rule for 10
It is the most easiest number to identify whether it is divisible by 10 , if the given number however large ends up with 0 then it is divisible by 0.
For Example
4546546546540 ,44545454560, 445474456110 5555598959550 are divisible by 10 as all the given numbers ends with 0.
and 445645489,454545,456445555 ,454545577 and 545454 are not divisible by 10 as all these numbers do not ends up with 0.
Conclusion
Thanks for giving your valuable time to read this post of the divisibility rules and divisibility test rules for divisibility rule for 2 , divisibility rule for 3, divisibility rule of 4 etc . If you liked this post , Then share it with your friends and family members . You can also read my others articles on Mathematics Learning and understanding Maths in easy ways.
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