Divisibility Rule of 97

The divisibility rule for 97 is a method by which we can find out if a number is divisible by 97 or not without using the division method. Check whether 4858 is divisible by 97 with the divisibility rule.
 

Step 1: Multiply the last digit of the number by 29, here in 4858, 8 is the last digit, multiply it by 29. 8 × 29 = 232.
 

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 485–232 = 253.
 

Step 3: As it is shown that 253 is a multiple of 97, therefore, the number is divisible by 97. If the result from step 2 isn't a multiple of 97, then the number isn't divisible by 97.
 

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 97.
 

• Know the multiples of 97: Memorize the multiples of 97 (97, 194, 291, … etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 97, then the number is divisible by 97.
   
• 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 97.
  
  For example: Check if 7823 is divisible by 97 using the divisibility test.
  
  Multiply the last digit by 29, i.e., 3 × 29 = 87. Subtract the remaining digits excluding the last digit by 87, 782–87 = 695. Still, 695 is a large number, hence we will repeat the process again and multiply the last digit by 29, 5 × 29 = 145.
  
  Now subtracting 145 from the remaining numbers excluding the last digit, 69–145 = -76. As -76 is negative, we consider it as 76. As 76 is not a multiple of 97, 7823 is not divisible by 97.
   
• Use the division method to verify: Students can use the division method as a way to verify and crosscheck 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.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 97 are 97, 194, 291, 388...
   
• Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
   
• Division method: The process of dividing a number by another number to check for divisibility, used as a verification tool.