Divisibility Rule of 13

The divisibility rule of 13 will help us to check if a number is divisible by 13 without any remainder. This means that a number is said to be divisible by 13 only when the remainder is ‘0’, where the quotient is a whole number. Now, to check for the divisibility of 13, you need to follow some rules. There are four rules to be followed. Let’s discuss them in detail.
 

Here, we group the digits of the number starting from the unit's place. Instead of dividing the number altogether, we split the digits into groups and perform a series of steps to get the result. Follow the steps given below to check if 13039 is divisible by 13:-

Step 1: Split the number, 13039 into 130 and 39 from the extreme right side.

Step 2: Subtract the first two digits of the given number from the last three digits of the number. Here, we have to subtract 39 from 130, which is 91 (130 – 39 = 91)

Step 3: Now we have to check if 91 is divisible by 13. If 91 is completely divisible by 13, then the given number 13039 is divisible by 13.

Step 4: 91 is divisible by 13, which gives 7 as the quotient and 0 as the remainder
→ 91 ÷ 13 = 7.

Step 5: Now divide, 13039 by 13
→ 13039 ÷ 13 = 1003. 

Since the remainder is ‘0’, we can say that 13039 is divisible by 13.

According to this rule, the product obtained by multiplying the unit place digit by 4 is added to the rest of the number. If the sum is a multiple of 13, then the given number is divisible by 3. Follow the steps given below to get an idea. Let’s check if 624 is divisible by 13.

Step 1: Multiply the digit in the unit place of 624 by 4. Here, 6 is in the unit place. So multiplying 4 by 4 we get 4 × 4 = 16.

Step 2: Now add 16 to the rest of the number, which is 62. We will get the sum as 62 + 16 = 78.

Step 3: Divide 78 by 13 → 78 ÷ 13 = 6. Here the remainder is ‘0’

Step 4: Since dividing 78 by 13 leaves no remainder, 624 is completely divisible by 13 → 624  ÷ 13 = 48. 

Since the quotient is a whole number, the given number is divisible by 13.
 

In this, the last two numbers in the units and tens place get separated, and the remaining digits of the number are multiplied by 4. If the last two digits of the number and the product's subtracted value are ‘0’, then the given number is divisible by 13. Let’s take an example of the number 325.

Step 1: Pair the numbers as 3 and 25

Step 2: Multiply 3 by 4 to get 12 → 3× 4.

Step 3: Find the difference between the last two digits (25) and the product (12). We will get the difference as ‘13’ → 25-12=13.

Step 4: Check if the result (13) is divisible by 13. 13 ÷ 13 = 1, and the remainder is zero.

We can say that 325 is completely divisible by 13.
 

This rule checks for divisibility by multiplying the last digit of the number by 9 and subtracting it from the remaining number. If the result is 0 or a multiple of 13, then the number given is divisible by 13. Let’s take the example of 793

Step 1: The last digit of the number 572 is 2.

Step 2: Multiply 2 by 9 to get, 2 × 9 = 18.

Step 3: Subtract 18 from 57 to get 39

Step 4: Divide 39 by 13 to check if it is a multiple of 13. Dividing 39 by 13 we get 3
→ 39 ÷ 13 = 3. 

Since the subtracted value is a multiple of 13, we can say that 572 is divisible by 13.
 

If kids are familiar with the divisibility rules, it helps them solve math problems quickly. Now we will learn a few tips and tricks for the divisibility rule of 13

• Split the numbers into the groups

Group bigger numbers like 62257 from the right. For example, group the number 62257 as (62) and (257)

• Look for Multiples of 13

Learn the multiples of 13 at least 20. This will help you check the divisibility while using rule 2 which is mentioned in the previous section.

• Use of Division Method

Students can try directly dividing the given number by 13 to verify the result.
If the quotient is a whole number, the number is divisible by 13. If it is a decimal number, it is not divisible by 13
 

• Multiple: A number which is the product of multiplying one number by another. For example, the first few multiples of 11 are 11, 22, 33, 44, 55, etc.

• Divisibility: The process of checking if a number is completely divisible by another. For example, to check if a number is divisible by 5, we will check if the last digit of the number is either ‘0’ or ‘5’. 

• Remainder: The leftover number that cannot be divided anymore by the divisor. For example, dividing 27 by 4 leaves you a remainder of 3.

• Subtraction: A mathematical method to find the difference between two numbers.