Divisibility Rules 1 to 20

Published by Kabir Chibber on October 10, 2020October 10, 2020

Divisibility rules 1 to 20 allow us to identify whether a particular number can be divided by another number. They save us time during exams and in real-life scenarios. They also help in calculating HCF and LCM quickly as we know which numbers will be divided and which won’t. The Divisibility rules 1 to 20 are the most important. Almost all numbers are divisible by these numbers, and those that are not divisible tend to be prime numbers or extremely large numbers. Some examples are given at the end, but for now let’s look at the divisibility rules 1 to 20.

The following is a list of divisibility rules 1 to 10 as they are the most common:

List of Divisibility Rules 1 to 20

1. Divisibility of 1- Every single number is divisible by one. When you divide a number by one, the result is the number itself.
2. Divisibility of 2 – A number is divisible by 2 if the digit in the ones place is an even number.
3. Divisibility of 3 – A number is divisible by 3 if the sum of all the digits is divisible by 3.
4. Divisibility of 4 – A number is divisible by 4 if the number formed by the digits in the place value of tens and ones is divisible by 4.
5. Divisibility of 5 – A number is divisible by 5 if the digit in the ones place value is 5 or 0.
6. Divisibility of 6 – A number is divisible by 6 if the number is divisible by both 2 and 3.
7. Divisibility of 7 – A number is divisible by 7 if the difference between twice the value of the digit in the ones place and the number formed by the rest of the digits is 0 or a multiple of 7.
8. Divisibility of 8 – A number is divisible by 8 if the number formed by the digits in the place value of hundreds, tens and ones is divisible by 8.
9. Divisibility of 9 – A number is divisible by 9 if the sum of all the digits is divisible by 9.
10. Divisibility of 10 – A number is divisible by 10 if the digit in the ones place value is 0.

Divisibility rules for 11 to 20 are important, but it is less likely that you will encounter situations that will require the use of these divisibility rules. The divisibility rules for 11 to 20 are:

1. Divisibility of 11 – A number is divisible by 11 if the difference between the sum of the digits in the odd place value and even place value is 0 or a multiple of 11.
2. Divisibility of 12 – A number is divisible by 12 if the number is divisible by both 3 and 4.
3. Divisibility of 13 – A number is divisible by 13 if the sum of the digit in the one’s place value, when multiplied by 4, and the number formed by the rest of the digits is 0 or a multiple of 13. (if abcde is a number divisible by 13, then abcd + 4e = 0 or a multiple of 13)
4. Divisibility of 14 – A number is divisible by 14 if the number is divisible by both 2 and 7.
5. Divisibility of 15 – A number is divisible by 15 if the number is divisible by both 3 and 5.
6. Divisibility of 16 – A number is divisible by 16 if the number formed by the last four digits is divisible by 16.
7. Divisibility of 17 – A number is divisible by 17 if the difference between five times the digits in the ones place value and the number formed by the rest of the digits is 0 or a multiple of 17.
8. Divisibility of 18 – A number is divisible by 18 if the number is divisible by both 2 and 9.
9. Divisibility of 19 – A number is divisible by 19 if the sum of the digit in the ones place value multiplied by 2 and the number formed by the rest of the digits is a multiple of 19.
10. Divisibility of 20 – A number is divisible by 20 if the number ends with 00,20,40,60 or 80.

Please remember that there are no divisibility rules for 1. Every number is divisible by 1.

Sample Questions

Here is an example in which we use divisibility rules to make our lives easier:

Q1. John has 33 oranges. Can he group them into bag such that there are 3 oranges in every bag?

Answer: Yes, he can group them in such a way. This is because the divisibility rule of 3 says “a number is divisible by 3 if the sum of all the digits is divisible by 3”. So in this situation, 3+3=6 which is divisible by 3, so the entire number is divisible by 3.

Q2. Samuel would like to give each of his friends equal amounts of balloons. If he has 82 balloons, can he give it to 6 of his friends?

Answer: No, he cannot give equal amounts of balloons to all his friends, because the divisibility rule of 6 says that the number must be divisible by 2 and 3. In this case, 82 is divisible by 2 (2 is an even number) however, it is not divisible by three as 8+2=10 and 10 is not divisible by 3.

Q3. Noah baked 77 cookies. He wants to distribute them equally with 7 of his neighbours. Is it possible to distribute the cookies equally?

Answer: Yes, it is possible to distribute the cookies equally, as the divisibility rules of 7 says: A number is divisible by 7 if the difference between twice the value of the digit in the ones place and the number formed by the rest of the digits is 0 or a multiple of 7. In this case, 7 is the ones digit of 77. So, 7 x 2= 14. Now, 14 – 7 = 7. Here, 7 is obviously divisible by 7, therefore the entire number is divisible by 7.

Q4. Find the HCF of 184 and 20.

Answer: As we said before, divisibility rules help in calculating HCF. In this case, we know that both these numbers are divisible by 4, by applying the divisibility rule of 4, which is: A number is divisible by 4 if the number formed by the digits in the place value of tens and ones is divisible by 4. With this simple trick, we now know our HCF is 4. To learn what HCF and LCM are and how to calculate them, you can check out this article.

For more practice questions, you can view this quiz