Divisibility rules for 13‌

The divisibility rules are useful in solving the large numbers division question easily. These rules are used to check whether the dividend can be completely divided by the divisor or not. For example, suppose any large number is to be divided by 13. Then, you can apply the divisibility rules and check whether the number is divisible or not without doing the actual lengthy division process and getting nothing in return. Thus, it saves your time very much.

For example, let us take a number, say 150. It needs to be divided by 6. The divisibility rule for 6 states that if the given number is divisible by both 2 and 3, then the number is also divisible by 6. In the case of 150, it is divisible by both 2 and 3. Hence it’s divisible by 6 too, giving 25 as an answer. Let’s take another example of 160. 160 is divisible by 2, but it is not divisible by 3. Therefore, it does not satisfy both the conditions required for the divisibility of 6. Hence it is not divisible by 6. So the nearest number to 160, which are divisible by 6, are 156 and 162, both being divisible by 2 and 3.

Divisibility rules for 13

There are 4 divisibility rules for 13 in total. They are:

Divisibility rule 1:

For a given integer, form alternating sums of blocks of three numbers from the right while moving towards the left. For instance, suppose there is a number N, if the number is formed by the alternative sum and difference of blocks of three digits from right to left, and is divisible by 13, then the number N is also said to be divisible by 13.

Example 1:

Take the number 2,453,674. Let us find out whether it is divisible by 13 or not.

Solution: By applying mentioned above,

674 - 453 + 2 = 223, which is not divisible by 13

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

Example 2:

Let us take another number, 1,139,502. Again, we need to find out whether it is divisible by 13 or not.

Solution: By applying mentioned above,

502-139+1 = 364 is divisible by 13

364 / 13 = 28

Therefore, 1,139,502 is divisible by 13

Divisibility rule 2:

We need to multiply the digit in the unit place by 4. Then, add the product with the rest of the numbers present to the left of the unit place. If the number that comes, as a result, is 0 or a multiple of 13, then the number is divisible by 13.

Example 3:

Take the number 962. Let us do the drill.

Solution: By applying mentioned above,

962 = 96 + (2 x 4) = 104 is divisible by 13

104 / 13 = 8

Therefore, 962 is divisible by 13

Divisibility rule 4:

Take the last two digits of the given integer. Then, subtract it from the 4 times of the rest of the number. If the number that comes, as a result, is 0 or a multiple of 13, we can conclude that the given integer is divisible by 13.

Example 4:

Find out whether 1157 is divisible by 13 or not.

Solution: By applying the above mentioned rule,

1157= (11 x 4) - 57 = -13 is divisible by 13

-13 / 13 = -1

Therefore, 1157 is divisible by 13

Divisibility rule 5:

In this rule, we need to multiply the last digit of the given number by 9. Then subtract the number from the rest of the number. If the result is divisible by 13, then the given number is divisible by 13.

Example 5:

Find out whether 11557 is divisible by 13 or not.

Solution: By applying the above mentioned rule,

11557= 1155 – (7 x 9) = 1092 is divisible by 13

1092= 109 – (2 x 9) = 91 is divisible by 13

91 / 13 = 7

Therefore, 11557 is divisible by 13

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