Divisibility Rule of 37

The divisibility rule for 37 is a method by which we can find out if a number is divisible by 37 or not without using the division method. Check whether 111 is divisible by 37 with the divisibility rule.

Step 1: Multiply the last digit of the number by 3, here in 111, 1 is the last digit; multiply it by 3. 1 × 3 = 3  

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 11 - 3 = 8.  

Step 3: As 8 is not a multiple of 37, 111 is not divisible by 37. If the result from step 2 is a multiple of 37, then the number is divisible by 37.
 

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 37.

• Know the multiples of 37: Memorize the multiples of 37 (37, 74, 111, 148, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 37, then the number is divisible by 37.

• Use negative numbers: If the result after subtraction is negative, consider its absolute value 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 37.
  
  For example: Check if 1480 is divisible by 37 using the divisibility test.  
  
  Multiply the last digit by 3, i.e., 0 × 3 = 0.  
  
  Subtract the result from the remaining digits excluding the last digit, 148 - 0 = 148.  
  
  Still, 148 is a large number, so we will repeat the process. Multiply the last digit by 3, 8 × 3 = 24.  
  
  Now subtract 24 from the remaining numbers excluding the last digit, 14 - 24 = -10.  
  
  The absolute value of -10 is not a multiple of 37, so 1480 is not divisible by 37.
   
• 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. For example, a number is divisible by 2 if it ends with an even digit.
   
• Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 37 are 37, 74, 111, 148, and so on.
   
• Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
   
• Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
   
• Absolute value: The absolute value of a number is its non-negative value without regard to its sign.