Divisibility Rule for 13

The divisibility rule for 13 is useful when you want to determine whether a number is fully divided by 13 or not. By knowing the divisibility by 13 we can easily say the result without dividing numbers. So get to know about the divisibility test for the 13 rule, examples and steps on how to check the divisibility rule of 13.

What is the Divisibility Rule for 13?

There are 4 different types of divisibility rules for 13. Each of them is given here:

1st Rule:

The divisibility rule for 13 states that a number is divisible by thirteen if the end digit of the number is multiplied by 4 and the product is added to the remaining number either giving 0 or a multiple of 13. In simple words the sum of the 4 times the last digit and the rest of the number is divided by 13, then the number is divisible by 13.

2nd Rule:

According to the rule, subtract the last 2 digits of the numbers from the 4 times the remaining number. If the difference is divisible by 13, then the number is divisible by 13.

3rd Rule:

Multiply the end digit of the number by 9 and subtract the product from the rest of the number. If the difference is a multiple of 13, then the original number is divisible by 13.

4th Rule:

For a given number, form alternating sum of blocks of 3 numbers from the right to left is divisible by 13, then the number is divisible by 13.

Procedure to Test if Number is Divisible by 13

Below listed are the instructions to tell that a number is divisible by 13 by observing their digits.

  • Take a large number for the divisibility test of 13.
  • Multiply the last digit of the number with 4.
  • Add the product to the remaining portion of the number.
  • Repeat the process until you get a two-digit number.
  • If it is a multiple of 13, then the given number is divisible by 13.

What numbers are divisible by 13

List of Numbers divisible by 13: The Numbers 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, 663, 676, 689, 702, 715, 728, 741, 754, 767, 780, 793, 806, 819, 832, 845, 858, 871, 884, 897, 910, 923, 936, 949, 962, 975, 988, 1001, 1014, 1027, 1040, 1053, 1066, 1079, 1092, 1105, 1118, 1131, 1144, 1157, 1170, 1183, 1196, 1209, 1222, 1235, 1248, 1261, 1274, 1287, 1300, etc. are divisible by 13.

Solved Questions on Divisibility Test of 13

Question 1:

Is 50661 divisible by 13?

Answer:

Given number is 50661

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

The remaining number is 5066

Addition = 5066 + 4 = 5070

Again, 4 times of the end digit = 0 x 4 = 0

Addition = 507 + 0 = 507

Again, 4 times of the end digit = 7 x 4 = 28

Addition = 50 + 28 = 78

78 is divisible by 13

So, 50661 is divisible by 13

Question 2:

Find the smallest 4-digit number that is divisible by 13.

Answer:

The smallest 4-digit number is 1000

Subtract the last two digits from the product of the 4 times of remaining number.

The last 2 digits are 00

4 times of remaining number = 4 x 10 = 40

Subtraction = 40 - 00 = 40

40 is not divisible by 13 so 1000 is not divisible by 13

So, check for the next number i.e 1001

The last 2 digits are 01

4 times of remaining number = 4 x 10 = 40

Subtraction = 40 - 1 = 39

As 39 is divisible by 13, 1001 is also divisible by 13

Therefore the smallest 4-digit number divisible by 13 is 1001.

FAQs on Divisibility of 13

How to find 13 multiples?

You have to check the divisibility rule of 13 to know whether the number is a multiple of 13 or not. The multiples of 13 are 13, 26, 39, 52, 65, 78, 91, etc.

What are the factors of 13?

Factors of 13 are 1 and 13.

Why does the divisibility rule for 13 work?

The divisibility rule is any number whose sum of the four times the last digit and remaining digits are divisible by 14, then the number is also divisible by 13.

Final Verdict

I hope that the info provided above regarding the divisibility rule for 13 is useful for you. Stay in touch with our site RoundingCalculator.guru to know more about divisibility rules.