Divisibility Rule of 823

The divisibility rule for 823 is a method by which we can find out if a number is divisible by 823 or not without using the division method. Check whether 8230 is divisible by 823 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 3. Here in 8230, 0 is the last digit, so multiply it by 3. 0 × 3 = 0.  

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 823 - 0 = 823.  

Step 3: As it is shown that 823 is a multiple of 823, therefore, the number is divisible by 823. If the result from step 2 isn't a multiple of 823, then the number isn't divisible by 823.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 823.

Know the multiples of 823:  

Memorize the multiples of 823 (823, 1646, 2469, 3292, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 823, then the number is divisible by 823.

Use 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 823.  
For example: Check if 16460 is divisible by 823 using the divisibility test.  
Multiply the last digit by 3, i.e., 0 × 3 = 0.  
Subtract the remaining digits excluding the last digit by 0, 1646 - 0 = 1646.  
Still, 1646 is a large number, hence we will repeat the process again and multiply the last digit by 3, 6 × 3 = 18.  
Now subtracting 18 from the remaining numbers excluding the last digit, 164 - 18 = 146.  
As 146 is a smaller number than 823, we need to continue the process, but since this example doesn't demonstrate divisibility, it's clear 16460 is not divisible by 823.

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 823 are 823, 1646, 2469, 3292, 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.
   
• Verify: The process of checking calculations by using another method, like division, to ensure correctness.