Find Divisibility Rule of Any Number in Seconds | Divisibility Rules

Divisibility Rules or Divisibility Tests were developed in order to make the division process simple and quicker, such that if we have to check whether a number is divisible by some other number, using these rules we can check the same without the long division method. These divisibility rules save us a lot of time either in finding factors using prime factorization or doing calculations in competitive or academic examinations
Divisibility Rule of 1:
As all the numbers are divisible by 1 so it doesn’t need any test to determine that. Any number k can be written as k×1, thus we can divide k by 1 and still have k left. For example, if 2341 is divided by 1, we have 2341 as the quotient and 0 as the remainder.
Divisibility Rule of 2:
A number is divisible by 2 if the last digit of the number is any of the following digits 0, 2, 4, 6, 8. The numbers with the last digits 0, 2, 4, 6, and 8 are called even numbers.
Example: 2580, 4564, 90032 etc. are divisible by 2.
Divisibility Rule of 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 90453 (9 + 0 + 4 +5 + 3 = 21) 21 is divisible by 3. 21 = 3 × 7. Therefore, 90453 is also divisible by 3.
Divisibility Rule of 4:
A number is divisible by 4 if the last two digits are divisible by 4.
Example: 456832960, here the last two digits are 60 that are divisible by 4 i.e.15 × 4 = 60. Therefore, the total number is divisible by 4.
Divisibility Rule of 5:
A number is divisible by five if the last digit of that number is either 0 or 5
Divisibility Rule of 6:
A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 10008, have 8 at one’s place so is divisible by 2 and the sum of 1, 0, 0, 0 and 8 gives the total 9 which is divisible by 3. Therefore, 10008 is divisible by 6.
Divisibility Rule of 7:
Following are the steps to check the divisibility rule for 7,
Take the last digit and then double the last digit.
Subtract the result from the remaining number.
If the number is 0 or a multiple of 7, then the original number is divisible by 7. Else, it is not divisible by 7.
Divisibility Rule of 11:
To check the divisibility rule for 11, if the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
Example: Consider a number to test the divisibility with 11, 264482240 mark the even place values and odd place values. Sum up the digits in even place values together and sum up the digits in odd place values together.
Digits
Place Value
2
0
6
1
4
2
4
3
8
4
2
5
2
6
4
7
0
8
Now sum up the digits in even place values i.e., 0th + 2th + 4th + 6th + 8th = 2 + 4 + 8 + 2 + 0 = 14. To add up the digits in odd place values i.e., 1th+ 3th + 5th + 7th = 6 + 4 + 2 + 4 = 14
Now calculate the difference between the sum of digits in even place values and the sum of digits in odd place values if the difference is divisible by 11 the complete number i.e., 264482240 is divisible by 11. Here the difference is 0, (14-14) which is divisible by 11. Therefore, 264482240 is divisible by 11.
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Chapters:
0:00 - Intro
0:48 - Divisibility Test of 13
1:25 - Example 1
2:22 - Divisibility Test of 19
2:47 - Example 2
3:57 - Outro
Editor: Parash Soni
Voice: Piyush Soni
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