Divisibility Rules For 13

Divisibility rules are basically to solve problems related to integer division in a very easy way. The divisibility rule has come to check whether the dividend integer can be completely divided by any other divisor integer or not.

In order to check the divisibility of a large number by interest will take about time. That's why counter-time divisibility rules were introduced. So, in this article, we are going to discuss divisibility rules for 13. 

Apart from 13, there are divisibility rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on.

For Example:

Divisibility by 4 rule, 48 in a number which is completely divided by 4 as the sum of the last two digits of the number is divided by 4. Let's find another number 47, which is not divisible by 4 as the sum of the last two digits of the number is not completely divided by 4. Using this simple rule, we can find if any number is divisible by 4 or not. 

Now, let's discuss the divisibility rule for 13, using definitions and examples.

Different Divisibility Rules For 13

We have to read 4 different types of divisibility rules for 13. Let us explain to you with examples one by one. 

Divisibility Rule 1: 

For a given number, form alternating sums of blocks of three numbers from the right and move towards the left. Suppose (n1, n2, n3, n4, n5, n6.....)  is a number N, then if the number formed by the alternative sum of blocks of 3-3 digits from right to left (n1, n2, n3, -  n4, n5, n6, + …. ) is divisible by 13, then the number N is additionally divisible by 13.

Example: Let a number is 2,453,674. Find out whether it is divisible by 13 or not.

Solution: By applying Rule 1,674 - 453 + 2 = 223 is not divisible by 13 

Therefore, 2,453,674 also is not divisible by 13

Divisibility Rule 2:

If a number N is given, then multiply the last digit of N with 4 and add it to the rest truncate of the number. If the result is divisible by 13, then the number N is additionally divisible by 13.

Example: Let a number be 780. Find whether it is divisible by 13.

Solution: By applying Rule 2,780: 78 + 0 x 4 = 78 and, number 78 is divisible by 13 and gives divisor as 6. 

Therefore, 780 is also divisible by 13.

Divisibility Rule 3:

For a number N, to check whether it is divisible by 13 or not, subtract the last 2 digits of the number N from the 4 times multiple of the rest of the number.

Example: Let a number is 728. Check whether it is divisible by 13 or not.

Solution: By implementing the divisibility rule of 13, we get,2197: 21 x 4 - 97 = 97 - 84 = 13, and number 13 is divisible by 13, giving the result as 0.

Divisibility Rule 4: 

Multiply the last digit by 9 of a number N and subtract it from the rest of the number. If the result is divisible by 13, then the numeral N is also divisible by 13.

Example: If a number is 858 then find out whether it is divisible by 13 or not. 

Solution: By applying rule 4,936: 93 - 6 x 9 = 39, and 39 is divisible by 13Therefore, 936 is divisible by 13.

Questions:

Question 1.

(a).  Is 298 divisible by 13? 

Ans.    

Four times of the last digit  = 4 x 8 = 32             

Remaining left 29             

Addition = 29 + 32 = 61             

Since 61 is not divisible by 13             

∴  298 is not divisible by 13.

(b).  Is 247 Divisible by 13?

Ans. Four times of the last digit  = 4  x 7 = 28            

Remaining left 24            

Addition = 24 + 28 = 52            

 Since 52 is divisible by 13             

∴  247 is divisible by 13.

(c).  Is 317 Divisible by 13? 

Ans.  Four times of the last digit  = 4 x 7 = 28            

Remaining left 31            

Now, Addition = 28 + 31 = 59            

Since 59 is not divisible by 13                   

∴317 is not divisible by 13.

(d). Is 50661 Divisible by 13? 

Ans.   

Four times of the last digit = 4  x 1 = 4            

Remaining left 5066            

Now, Addition = 5066 + 4 = 5070            

Again, Four times of the last digit = 4  x 0 = 0            

Now, Addition = 507 + 0 = 507            

Again, Four times of the last digit = 4 x 7 = 28            

Now,  Addition = 50 + 28 = 78                

And, 78 is divisible by 13 at 13 x 6.

The concept of divisibility rules is introduced in the third grade. First, the students are taught about BODMAS. The concept of multiplication and division is elaborated in the higher classes. When students enter fourth grade they are taught about factors and multiples and prime factorization and composite numbers and integers. All these concepts form the basic foundation of mathematics and it is extremely important to have a good hold over these topics in order to get a higher grade in the class and it is only after understanding these topics that a student can go for higher studies.

The expert mathematical team at Vedantu has curated all the study material related to divisibility rules and this article mainly deals with divisibility rules for 13. Students can find many other divisibility rules for different numbers as per their needs. This article explains in-depth what the divisibility rule is and why we use these rules. In order to get a concrete hold over the concept Vedantu’s team has also provided practice questions along with their solutions so that students can learn and understand in an easier way.

Why study divisibility rules?

These divisibility rules are tricks in mathematics that help students to play, manipulate numbers and also help in solving the problems in an easier and more efficient way. These divisibility rules help in improving mathematical skills. In order to use the divisibility rules, students should get a good hold over the divisibility concept before they can use these tricks or divisibility rules in their favor. Students should fully understand when and how to use these rules. The rules of divisibility are extremely important in the study of mathematics as it makes problem-solving easier. Students should be equipped with this concept as early as possible as it will only make them mentally strong and therefore will enable them to get an edge over the others.

These rules help students to build a number sense and help them to deal effectively with large numbers that usually scare students. The goal is to help students be familiar with the numbers and be flexible while working with them.

Divisibility rules help you to understand if a number is divisible by a certain number for example 3, 2, 4, etc. without actually using division or a Calculator.

The best possible way to learn divisibility rules is by repeatedly using them every day during homework or in the classroom as this will help in getting the concept and repeatedly using it is the only possible way by which a student can effectively learn these divisibility rules.