Divisibility Rule of 523

The divisibility rule for 523 is a method by which we can find out if a number is divisible by 523 or not without using the division method. Check whether 1046 is divisible by 523 using the divisibility rule.

Step 1: Multiply the last digit of the number by 104, here in 1046, 6 is the last digit, so multiply it by 104. 6 × 104 = 624.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit, i.e., 104 – 624 = -520.

Step 3: As it is shown that -520 is a multiple of 523 (since -520 + 1046 = 526, which is a multiple of 523), therefore, the number is divisible by 523. If the result from Step 2 isn't a multiple of 523, then the number isn't divisible by 523.

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 523.

Know the multiples of 523:

Memorize the multiples of 523 (523, 1046, 1569, 2092, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 523, then the number is divisible by 523.

Use negative numbers:

If the result we get after the subtraction is negative, we will 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 523. For example, check if 2092 is divisible by 523 using the divisibility test. Multiply the last digit by 104, i.e., 2 × 104 = 208. Subtract the remaining digits excluding the last digit by 208, 209 – 208 = 1. Since 1 + 523 = 524, which is not a multiple of 523, 2092 is not divisible by 523.

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 verify and also learn.

• Divisibility rule: A set of rules used to determine whether a number is divisible by another number. For example, a number is divisible by 2 if the number ends with an even number.

• Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 523 are 523, 1046, 1569, etc.

• Integers: Integers are numbers that 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.

• Negative numbers: Negative numbers are numbers less than zero and are considered in absolute value for divisibility checks