Divisibility Rule of 23

The divisibility rule for 23 is a method by which we can find out if a number is divisible by 23 or not without using the division method. Check whether 276 is divisible by 23 with the divisibility rule.

Step 1: Multiply the last digit of the number by 7, here in 276, 6 is the last digit, multiply it by 7. 6 × 7 = 42.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 27 - 42 = -15.

Step 3: As it is shown that -15 is not a multiple of 23, therefore, the number is not divisible by 23. If the result from Step 2 is a multiple of 23, then the number is divisible by 23.

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 23.

• Know the multiples of 23: Memorize the multiples of 23 (23, 46, 69, 92, 115…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 23, then the number is divisible by 23.

• 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 23.
  
  For example: Check if 4603 is divisible by 23 using the divisibility test. Multiply the last digit by 7, i.e., 3 × 7 = 21.
  
  Subtract the remaining digits excluding the last digit by 21, 460 - 21 = 439. Still, 439 is a large number, hence we will repeat the process again and multiply the last digit by 7, 9 × 7 = 63.
  
  Now subtracting 63 from the remaining numbers excluding the last digit, 43 - 63 = -20. As -20 is not a multiple of 23, 4603 is not divisible by 23.

• 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. For example, a number is divisible by 23 if the divisibility rule confirms it.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 23 are 23, 46, 69, 92, 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: The process of checking the accuracy of calculations, often using different methods such as actual division.