Divisibility Rule of 233

The divisibility rule for 233 is a method by which we can find out if a number is divisible by 233 or not without using the division method. Check whether 466 is divisible by 233 with the divisibility rule.

Step 1: Multiply the last digit of the number by 7 (a key component of 233), here in 466, 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., 46 - 42 = 4.

Step 3: As it is shown that 4 is not a multiple of 233, therefore, the number is not divisible by 233. If the result from step 2 is a multiple of 233, then the number is divisible by 233.

Learn the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 233.

Know the multiples of 233:  

Memorize the multiples of 233 (233, 466, 699, 932, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 233, then the number is divisible by 233.

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 233.  
For example: Check if 932 is divisible by 233 using the divisibility test.  

Multiply the last digit by 7, i.e., 2 × 7 = 14.  

Subtract the remaining digits excluding the last digit by 14, 93 - 14 = 79.  

Repeat the process: Multiply the last digit of 79 by 7, i.e., 9 × 7 = 63.  

Subtract the remaining digits excluding the last digit by 63, 7 - 63 = -56.  

As 56 is not a multiple of 233, 932 is not divisible by 233.

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 2 if the number ends with even numbers.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 233 are 233, 466, 699, 932, 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 if calculations or results are accurate, often using an alternate method like division to confirm.