Divisibility Rule of 337

The divisibility rule for 337 is a method by which we can find out if a number is divisible by 337 or not without using the division method. Let's explore whether 1011 is divisible by 337 using this rule.  

Step 1: Multiply the last digit of the number by a specific constant. Here, in 1011, the last digit is 1. Multiply it by 112 (a constant derived for divisibility by 337).  

1 × 112 = 112  

Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 101 - 112 = -11.  

Step 3: Since -11 is not a multiple of 337, 1011 is not divisible by 337. If the result from Step 2 were a multiple of 337, then the number would be divisible by 337.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 337.

• Know the multiples of 337: Memorize the multiples of 337 (337, 674, 1011, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 337, then the number is divisible by 337.

• Use negative numbers: If the result we get 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 to determine divisibility by 337.  
  
  For example: Check if 101123 is divisible by 337 using the divisibility test.  
  
  Multiply the last digit by 112, i.e., 3 × 112 = 336.
  
  Subtract the remaining digits excluding the last digit by 336, 10112 - 336 = 9786.  
  
  Since 9786 is still large, repeat the process: Multiply the last digit by 112, 6 × 112 = 672.
  
  Now subtract 672 from the remaining numbers excluding the last digit, 978 - 672 = 306.
  
  Since 306 is not a multiple of 337, 101123 is not divisible by 337.

• 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: Results obtained after multiplying a number by an integer. For example, multiples of 337 are 337, 674, 1011, etc.

• Integers: Numbers that include all whole numbers, negative numbers, and zero.

• Subtraction: The process of finding the difference between two numbers by reducing one number from another.

• Constant: A specific number used as a multiplier in the divisibility rule for checking divisibility.