Divisibility Rule of 197

The divisibility rule for 197 is a method by which we can find out if a number is divisible by 197 or not without using the division method. Check whether 3941 is divisible by 197 using the divisibility rule.  

Step 1: Multiply the last digit of the number by 12, here in 3941, 1 is the last digit. Multiply it by 12: 1 × 12 = 12.  

Step 2: Subtract the result from Step 1 with the remaining values but do not include the last digit. i.e., 394–12 = 382.  

Step 3: If 382 is a multiple of 197, then the number is divisible by 197. If the result from Step 2 isn't a multiple of 197, then the number isn't divisible by 197.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 197.  

• Know the multiples of 197:  

Memorize the multiples of 197 (197, 394, 591, 788, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 197, then the number is divisible by 197.  

• 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 197.

 
For example: Check if 7882 is divisible by 197 using the divisibility test.  

Multiply the last digit by 12, i.e., 2 × 12 = 24.  

Subtract the remaining digits excluding the last digit by 24, 788–24 = 764.  

Still, 764 is a large number, so we will repeat the process. Multiply the last digit by 12, 4 × 12 = 48.  

Now subtracting 48 from the remaining numbers excluding the last digit, 76–48 = 28.  

Since 28 is not a multiple of 197, 7882 is not divisible by 197.

• 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.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 197 are 197, 394, 591, etc.

• Integers: Integers are numbers that 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: The process of checking if the result obtained is correct, often using another method like division.