Divisibility Rule of 223

The divisibility rule for 223 is a method by which we can find out if a number is divisible by 223 or not without using the division method. Check whether 446 is divisible by 223 with the divisibility rule.  

Step 1: Multiply the last digit of the number by 67, here in 446, 6 is the last digit, multiply it by 67. 6 × 67 = 402  

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 44 - 402 = -358.  

Step 3: Since -358 is not a multiple of 223, the number 446 is not divisible by 223. If the result from step 2 is a multiple of 223, then the number is divisible by 223.
 

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 223.

Know the multiples of 223:  

Memorize the multiples of 223 (223, 446, 669, ...etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 223, then the number is divisible by 223.

Use the negative numbers:  

If the result we get after the subtraction is negative, consider its absolute value 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 223.  
For example: Check if 669 is divisible by 223 using the divisibility test.  

Multiply the last digit by 67, i.e., 9 × 67 = 603.  

Subtract the remaining digits excluding the last digit by 603, 66 - 603 = -537.  

Since -537 is a multiple of 223, 669 is divisible by 223.

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 223 if the calculated result is a multiple of 223.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 223 are 223, 446, 669, 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.

• Absolute value: The absolute value of a number is the non-negative value of that number without regard to its sign. For example, the absolute value of both -537 and 537 is 537.