Divisibility Rule of 137

The divisibility rule for 137 is a method by which we can find out if a number is divisible by 137 or not without using the division method. Check whether 6849 is divisible by 137 with the divisibility rule.

Step 1: Multiply the last digit of the number by 5, here in 6849, 9 is the last digit, multiply it by 5. 9 × 5 = 45

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 684–45 = 639.

Step 3: If the result from Step 2 is a multiple of 137, then the number is divisible by 137. Otherwise, the number is not divisible by 137. In our example, 639 is not a multiple of 137, so 6849 is not divisible by 137.

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 137.

• Know the multiples of 137: Memorize the multiples of 137 (137, 274, 411, 548, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 137, then the number is divisible by 137.
   
• Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 137.
  
  For example, check if 54837 is divisible by 137 using the divisibility test.Multiply the last digit by 5, i.e., 7 × 5 = 35.Subtract the remaining digits excluding the last digit by 35, 5483–35 = 5448.Still, 5448 is a large number, hence we will repeat the process again and multiply the last digit by 5, 8 × 5 = 40.
  
  Now subtracting 40 from the remaining numbers excluding the last digit, 544–40 = 504.
  
  Since 504 is not a multiple of 137, 54837 is not divisible by 137.
   
• 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. For example, a number is divisible by 2 if the number ends with even numbers.
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 137 are 137, 274, 411, 548, 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: Using another method, such as actual division, to confirm the result obtained from the divisibility rule.