Divisibility Rule of 413

The divisibility rule for 413 is a method by which we can find out if a number is divisible by 413 or not without using the division method. Check whether 82600 is divisible by 413 with the divisibility rule.

Step 1: Multiply the last digit of the number by 124, here in 82600, 0 is the last digit, multiply it by 124. 0 × 124 = 0

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 8260 - 0 = 8260.

Step 3: As it is shown that 8260 is not a multiple of 413, therefore, the number is not divisible by 413. If the result from Step 2 is a multiple of 413, then the number is divisible by 413.

Learning the divisibility rule can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 413.

1. Know the multiples of 413:

Memorize the multiples of 413 (413, 826, 1239, 1652, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 413, then the number is divisible by 413.

2. Use the negative numbers:

If the result we get after the subtraction is negative, we will ignore the sign and consider it as positive for checking the divisibility of a number.

3. Repeat the process for large numbers:

Students should keep repeating the divisibility process until they reach a small number that is divisible by 413. For example, check if 165200 is divisible by 413 using the divisibility test.

Multiply the last digit by 124, i.e., 0 × 124 = 0.

Subtract the remaining digits excluding the last digit by 0, 16520 - 0 = 16520.

Still, 16520 is a large number, hence we will repeat the process again and multiply the last digit by 124, 0 × 124 = 0.
Now subtracting 0 from the remaining numbers excluding the last digit, 1652 - 0 = 1652.

As 1652 is a multiple of 413, 165200 is divisible by 413.

4. 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. 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 413 are 413, 826, 1239, 1652, etc.

• Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.

• Subtraction: Subtraction is the process of finding out the difference between two numbers by reducing one number from another.

• Verification: The process of confirming that the result obtained from applying the divisibility rule is correct, often done using direct division.