Divisibility Rule of 997

The divisibility rule for 997 is a method by which we can determine if a number is divisible by 997 without using the division method. Check whether 1994 is divisible by 997 with the divisibility rule.

Step 1: Multiply the last digit of the number by 3, here in 1994, 4 is the last digit, so multiply it by 3. 4 × 3 = 12

Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 199–12 = 187.

Step 3: Since 187 is not a multiple of 997, repeat the process. Multiply the last digit of 187 by 3, which is 7 × 3 = 21.

Step 4: Subtract 21 from the remaining digits, 18–21 = -3. As 3 is not a multiple of 997, 1994 is not divisible by 997.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 997.

Know the multiples of 997:

Memorize the multiples of 997 (997, 1994, 2991, etc.) to quickly check the divisibility. If the result from subtraction is a multiple of 997, then the number is divisible by 997.

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 to determine divisibility by 997. For example, check if 3988 is divisible by 997 using the divisibility test. Multiply the last digit by 3, i.e., 8 × 3 = 24. Subtract the remaining digits excluding the last digit by 24, 398–24 = 374. Repeat the process: multiply the last digit by 3, 4 × 3 = 12. Now subtract 12 from the remaining numbers excluding the last digit, 37–12 = 25. Since 25 is not a multiple of 997, 3988 is not divisible by 997.

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 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 997 are 997, 1994, 2991, etc.

• 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.

• Verification: The process of confirming the correctness of a result or calculation.