Divisibility Rule of 73

The divisibility rule for 73 is a method by which we can find out if a number is divisible by 73 or not without using the division method. Check whether 5843 is divisible by 73 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 4, here in 5843, 3 is the last digit, so multiply it by 4. 3 × 4 = 12.

 
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 584–12 = 572.  

Step 3: As shown, 572 is a multiple of 73, therefore, the number is divisible by 73. If the result from step 2 isn't a multiple of 73, then the number isn't divisible by 73.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 73. 

• Know the multiples of 73: Memorize the multiples of 73 (73, 146, 219, 292, 365…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 73, then the number is divisible by 73. 

• 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 73.  
  
  For example: Check if 10985 is divisible by 73 using the divisibility test.  
  
  Multiply the last digit by 4, i.e., 5 × 4 = 20  
  
  Subtract the remaining digits excluding the last digit by 20, 1098–20 = 1078  
  
  Still, 1078 is a large number, so we will repeat the process by multiplying the last digit by 4, 8 × 4 = 32.  
  
  Now subtract 32 from the remaining numbers excluding the last digit, 107–32 = 75.  
  
  As 75 is not a multiple of 73, 10985 is not divisible by 73. 

• Use the division method to verify: Students can use the division method as a way to verify and crosscheck 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 73 are 73, 146, 219, 292...

• 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 is the process of confirming the accuracy of a calculation or result, often through a different method such as division.