Divisibility Rule of 397

The divisibility rule for 397 is a method by which we can ascertain if a number is divisible by 397 without performing the division directly. Check whether 15881 is divisible by 397 using the divisibility rule.

Step 1: Multiply the last digit of the number by 17. In 15881, 1 is the last digit, so multiply it by 17. 1 × 17 = 17.

Step 2: Subtract the result from Step 1 from the remaining part of the number, excluding the last digit. That is, 1588 - 17 = 1571.

Step 3: Repeat the process for the result if necessary. For 1571, multiply the last digit (1) by 17, 1 × 17 = 17. Subtract from the remaining digits 157 - 17 = 140.

Step 4: Continue the process if necessary, but for this example, since 140 is not divisible by 397, 15881 is not divisible by 397.

Learning the divisibility rule helps kids master division. Let’s learn a few tips and tricks for the divisibility rule of 397.

• Know the multiples of 397: Memorize the multiples of 397 (397, 794, 1191, 1588, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 397, then the number is divisible by 397.
   
• Use the negative numbers: If the result after subtraction is negative, consider its absolute value for checking divisibility.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 397 or can clearly determine divisibility.
   
• 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 confirm their findings and also learn.

• Divisibility rule: A set of rules used to determine if a number is divisible by another number without performing division.
   
• Multiples: The results obtained after multiplying a number by an integer. For example, multiples of 397 are 397, 794, 1191, etc.
   
• Integers: Numbers that include all whole numbers, negative numbers, and zero.
   
• Subtraction: A mathematical process of finding the difference between two numbers by reducing one from the other.
   
• Absolute value: The non-negative value of a number without regard to its sign.