Divisibility Rule of 373

The divisibility rule for 373 is a method by which we can find out if a number is divisible by 373 or not without using the division method. Check whether 112,019 is divisible by 373 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 11, here in 112,019, 9 is the last digit. Multiply it by 11. 9 × 11 = 99.  

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 11201–99 = 11102.  

Step 3: Repeat the process of Step 1 and Step 2. Multiply the last digit of 11102 by 11, i.e., 2 × 11 = 22.  

Step 4: Subtract 22 from the remaining numbers excluding the last digit, 1110–22 = 1088.  

Step 5: Repeat the process again. Multiply the last digit of 1088 by 11, i.e., 8 × 11 = 88.
 
Step 6: Subtract 88 from the remaining numbers excluding the last digit, 108–88 = 20.
 
Step 7: Since 20 is not a multiple of 373, 112,019 is not divisible by 373. If the result from these steps is a multiple of 373, then the number is divisible by 373.
 

Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 373.  
 

• Know the multiples of 373: Memorize the multiples of 373 (373, 746, 1119, ...etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 373, then the number is divisible by 373.  
   
• 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 that is divisible by 373 or determine it is not divisible.  
   
• 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.  
   
• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 373 are 373, 746, 1119, ...
   
• Integers: Integers are numbers that include all 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: Verification involves checking the accuracy of a calculation or process, such as confirming divisibility using another method like division.