Divisibility Rule of 613

The divisibility rule for 613 is a method by which we can determine if a number is divisible by 613 without using the division method.

Check whether 1226 is divisible by 613 using the divisibility rule.  

Step 1: Multiply the last digit of the number by 2. In 1226, 6 is the last digit, so multiply it by 2. 6 × 2 = 12.  

Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 122–12=110.  

Step 3: Since 110 is not a multiple of 613, 1226 is not divisible by 613. If the result from step 2 is a multiple of 613, then the number is divisible by 613.

Learning the divisibility rule will help in mastering division. Let’s learn a few tips and tricks for the divisibility rule of 613.

• Know the multiples of 613: Memorize the multiples of 613 (613, 1226, 1839, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 613, then the number is divisible by 613.

• Use the negative numbers: If the result we get after the subtraction is negative, ignore the symbol and consider it as positive for checking the divisibility of a number.

• Repeat the process for large numbers: You should keep repeating the divisibility process until you reach a small number that is divisible by 613.  
  
  For example: Check if 18407 is divisible by 613 using the divisibility test.  
  
  Multiply the last digit by 2, i.e., 7 × 2 = 14.  
  
  Subtract the remaining digits excluding the last digit by 14, 1840–14=1826.  
  
  Still, 1826 is a large number, hence we will repeat the process again and multiply the last digit by 2, 6 × 2 = 12.  
  
  Subtracting 12 from the remaining numbers excluding the last digit, 182–12=170.  
  
  As 170 is not a multiple of 613, 18407 is not divisible by 613.

• Use the division method to verify: You can use the division method as a way to verify and crosscheck your results. This will help verify and also learn.

• Divisibility rule: The set of rules used to determine whether a number is divisible by another number. For example, a number is divisible by 2 if it ends with an even number.

• Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 613 are 613, 1226, 1839, etc.

• Integers: Integers include all whole numbers, negative numbers, and zero.

• Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.

• Verification: Verification is the process of confirming the result of a calculation or operation, often using an alternative method.