Divisibility Rule of 239

The divisibility rule for 239 is a method by which we can find out if a number is divisible by 239 or not without using the division method. Check whether 57317 is divisible by 239 with the divisibility rule.

Step 1: Multiply the last digit of the number by 477, here in 57317, 7 is the last digit, multiply it by 477. 7 × 477 = 3339  

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit, i.e., 5731–3339 = 2392.  

Step 3: As it is shown that 2392 is not a multiple of 239, therefore, the number is not divisible by 239. If the result from Step 2 was a multiple of 239, then the number would be divisible by 239.

Learning the divisibility rule will help students master division. Let’s learn a few tips and tricks for the divisibility rule of 239.

Know the multiples of 239:

Memorize the multiples of 239 (239, 478, 717, 956, 1195, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 239, then the number is divisible by 239.

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 239. For example, check if 114478 is divisible by 239 using the divisibility test. Multiply the last digit by 477, i.e., 8 × 477 = 3816. Subtract the remaining digits excluding the last digit by 3816, 11447–3816 = 7629. Still, 7629 is a large number, hence we will repeat the process again and multiply the last digit by 477, 9 × 477 = 4293. Now subtracting 4293 from the remaining numbers excluding the last digit, 762–4293 = -3531. Consider this as positive 3531. As 3531 is not a multiple of 239, 114478 is not divisible by 239.

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 239 are 239, 478, 717, 956, etc.

• Integers: Integers include all 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 accuracy of a result, often by using an alternative method, such as division, to ensure correctness.