197 LearnersLast updated on May 26th, 2025
Divisibility Rule of 457
The divisibility rule is a way to find out 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 457.
What is the Divisibility Rule of 457?
The divisibility rule for 457 is a method by which we can find out if a number is divisible by 457 or not without using the division method. Check whether 914 is divisible by 457 with the divisibility rule.
Step 1: Multiply the last digit of the number by 3. Here in 914, 4 is the last digit, so multiply it by 3. 4 × 3 = 12.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 91–12 = 79.
Step 3: As it is shown that 79 is not a multiple of 457, the number is not divisible by 457. If the result from Step 2 were a multiple of 457, then the number would be divisible by 457.
Tips and Tricks for Divisibility Rule of 457
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 457.
- Know the multiples of 457: Memorize the multiples of 457 (457, 914, 1371, 1828, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 457, then the number is divisible by 457.
- 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 457. For example: Check if 4572 is divisible by 457 using the divisibility test. Multiply the last digit by 3, i.e., 2 × 3 = 6. Subtract the remaining digits excluding the last digit by 6, 457–6 = 451. Still, 451 is not a large number, but let's repeat the steps for clarity. Multiply the last digit of 451 by 3, 1 × 3 = 3. Now subtracting 3 from the remaining numbers excluding the last digit, 45–3 = 42. As 42 is not a multiple of 457, 4572 is not divisible by 457.
- 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 457
The divisibility rule of 457 helps us quickly check if the given number is divisible by 457, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 3 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 457.
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 gotten a large number result after subtraction. The process should be repeated until we get the smallest number that is divisible by 457.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking the divisibility rules don't apply to the negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse the steps or forget the steps; to avoid the error, students should practice regularly.
Divisibility Rule of 457 Examples
Problem 1
Is 914 divisible by 457?
Yes, 914 is divisible by 457.
Explanation
Since 914 is a larger number, let’s verify using the divisibility rule for 457.
1) Take the last three digits of the number, which is 914.
2) Check if 914 is a multiple of 457. Yes, 914 is exactly 457 × 2.
Therefore, 914 is divisible by 457.
Problem 2
Check the divisibility rule of 457 for 1371.
Yes, 1371 is divisible by 457.
Explanation
To check if 1371 is divisible by 457:
1) Take the last three digits of the number, which is 371.
2) Subtract twice 457 from 1371. 1371 - 2 × 457 = 457.
3) The result is 457, which is a multiple of 457 itself, hence 1371 is divisible by 457.
Problem 3
Is -2285 divisible by 457?
Yes, -2285 is divisible by 457.
Explanation
To determine if -2285 is divisible by 457, ignore the negative sign and check 2285.
1) Take the last three digits, which are 285.
2) Subtract 457 from 2285. 2285 - 457 = 1828.
3) Subtract another 457 from 1828. 1828 - 457 = 1371.
4) Subtract another 457 from 1371. 1371 - 457 = 914.
5) Finally, 914 is 457 × 2, confirming divisibility.
Problem 4
Can 500 be divisible by 457 following the divisibility rule?
No, 500 isn't divisible by 457.
Explanation
To verify divisibility of 500 by 457:
1) Take the last three digits, which are 500.
2) Since 500 is less than 457, it can’t be a multiple of 457.
Thus, 500 is not divisible by 457.
Problem 5
Check the divisibility rule of 457 for 4570.
Yes, 4570 is divisible by 457.
Explanation
To check if 4570 is divisible by 457:
1) Take the last three digits, which are 570.
2) Subtract 457 from 4570. 4570 - 457 = 4113.
3) Subtract another 457 from 4113. 4113 - 457 = 3656.
4) Continue until you reach 0.
Since you reach 0, 4570 is divisible by 457.
FAQs on Divisibility Rule of 457
1.What is the divisibility rule for 457?
2.How many numbers are there between 1 and 1371 that are divisible by 457?
3.Is 1828 divisible by 457?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 457 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 457?
7.What are some fun ways kids in United States can practice Divisibility Rule of 457 with numbers?
8.What role do numbers and Divisibility Rule of 457 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 457 skills?
Important Glossaries for Divisibility Rule of 457
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 457 are 457, 914, 1371, etc.
- Integers: Integers are 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.
- Verification: Verification is the process of confirming that a result or calculation is correct by using another method, such as division.
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About BrightChamps in United States
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.
