Divisibility Rule

Divisibility rules are basically to solve problems related to integer division in a very easy way. 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 to 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 moving 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 is 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 13

Therefore, 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.