Divisibility Rule of 723

The divisibility rule for 723 is a method by which we can find out if a number is divisible by 723 without using the division method.

Check whether 1446 is divisible by 723 with the divisibility rule.

Step 1: Multiply the last digit of the number by 2. Here in 1446, 6 is the last digit, multiply it by 2. 6 × 2 = 12 

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 144–12 = 132.

Step 3: As it is shown that 132 is a multiple of 723, therefore, the number is divisible by 723. If the result from Step 2 isn't a multiple of 723, then the number isn't divisible by 723.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 723.

• Know the multiples of 723: Memorize the multiples of 723 (723, 1446, 2169, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 723, then the number is divisible by 723.
   
• 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 723. 
  
  For example: Check if 3615 is divisible by 723 using the divisibility test. Multiply the last digit by 2, i.e., 5 × 2 = 10.
  
  Subtract the remaining digits excluding the last digit by 10, 361–10 = 351. Still, 351 is a large number, hence we will repeat the process again. Multiply the last digit by 2, 1 × 2 = 2.
  
  Now subtracting 2 from the remaining numbers excluding the last digit, 35–2 = 33.
  
  As 33 is not a multiple of 723, 3615 is not divisible by 723.
   
• 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 723 are 723, 1446, 2169, 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: Verification is the process of confirming the validity of a calculation or result, often by using a different method such as division.