Divisibility Rule of 31

The divisibility rule for 31 is a method by which we can find out if a number is divisible by 31 or not without using the division method. Check whether 372 is divisible by 31 with the divisibility rule.

Step 1: Multiply the last digit of the number by 3, here in 372, 2 is the last digit. Multiply it by 3. 2 × 3 = 6.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 37 - 6 = 31.

Step 3: As it is shown that 31 is a multiple of 31, therefore, the number is divisible by 31. If the result from step 2 isn't a multiple of 31, then the number isn't divisible by 31.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 31.

• Know the multiples of 31:  Memorize the multiples of 31 (31, 62, 93, 124, 155, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 31, then the number is divisible by 31.
   
• Use the negative numbers:  If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
   
• Repeat the process for large numbers:  Students should keep repeating the divisibility process until they reach a small number that is divisible by 31.  
  
  For example: Check if 5893 is divisible by 31 using the divisibility test.  
  
  Multiply the last digit by 3, i.e., 3 × 3 = 9.  Subtract the remaining digits excluding the last digit by 9, 589 - 9 = 580.  
  
  Still, 580 is a large number, hence we will repeat the process again and multiply the last digit by 3, 0 × 3 = 0.  
  
  Now subtracting 0 from the remaining numbers excluding the last digit, 58 - 0 = 58.  58 is not a multiple of 31, so 5893 is not divisible by 31.
   
• Use the division method to verify:  Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

• Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 31 if the process described leads to a multiple of 31.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 31 are 31, 62, 93, 124, etc.
   
• Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is the process of finding out the difference between two numbers by reducing one number from another.
   
• Verification: The process of using division to confirm the result of a divisibility test.