211 LearnersLast updated on May 26th, 2025
Divisibility Rule of 523
The divisibility rule is a way to determine whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 523.
What is the 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.
Tips and Tricks for Divisibility Rule of 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.
Common Mistakes and How to Avoid Them in Divisibility Rule of 523
The divisibility rule of 523 helps us quickly check if a given number is divisible by 523, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes that will help you avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, multiplying the last digit by 104 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 523.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large number as the result after subtraction. The process should be repeated until we get the smallest number that is divisible by 523.
Mistake 4
Not considering the negative values.
Students might disregard negative values, thinking divisibility rules don't apply to negative values. But the divisibility rule is applicable for negative values too. Therefore, students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse or forget the steps. To avoid errors, students should practice regularly.
Divisibility Rule of 523 Examples
Problem 1
Is 1569 divisible by 523?
Yes, 1569 is divisible by 523.
Explanation
To check divisibility by 523, we can directly divide the number.
1) Divide 1569 by 523, resulting in 1569 ÷ 523 = 3.
2) The result is a whole number with no remainder, which means 1569 is divisible by 523.
Problem 2
Check the divisibility of 2615 by 523.
Yes, 2615 is divisible by 523.
Explanation
We use basic division to check divisibility.
1) Divide 2615 by 523, resulting in 2615 ÷ 523 = 5.
2) Since the division results in a whole number without any remainder, 2615 is divisible by 523.
Problem 3
Is 1046 divisible by 523?
No, 1046 is not divisible by 523.
Explanation
We verify divisibility through direct division.
1) Divide 1046 by 523, resulting in 1046 ÷ 523 = 2 with a remainder.
2) As there is a remainder after division, 1046 is not divisible by 523.
Problem 4
Can 5230 be divisible by 523?
Yes, 5230 is divisible by 523.
Explanation
Check divisibility through division.
1) Divide 5230 by 523, resulting in 5230 ÷ 523 = 10.
2) The division results in a whole number with no remainder, indicating 5230 is divisible by 523.
Problem 5
Is 4024 divisible by 523?
No, 4024 is not divisible by 523.
Explanation
Use division to check for divisibility.
1) Divide 4024 by 523, resulting in 4024 ÷ 523 = 7 with a remainder.
2) Since there is a remainder, 4024 is not divisible by 523.
FAQs on Divisibility Rule of 523
1.What is the divisibility rule for 523?
2. How many numbers are there between 1 and 2000 that are divisible by 523?
3. Is 1046 divisible by 523?
4. What if I get 0 after subtracting?
5.Does the divisibility rule of 523 apply to all integers?
6.How can children in Philippines use numbers in everyday life to understand Divisibility Rule of 523?
7.What are some fun ways kids in Philippines can practice Divisibility Rule of 523 with numbers?
8.What role do numbers and Divisibility Rule of 523 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Divisibility Rule of 523 skills?
Important Glossaries for Divisibility Rule of 523
- 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
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About BrightChamps in Philippines
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
