118 LearnersLast updated on May 26th, 2025
Divisibility Rule of 57
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 57.
What is the Divisibility Rule of 57?
The divisibility rule for 57 is a method by which we can find out if a number is divisible by 57 or not without using the division method. Check whether 285 is divisible by 57 with the divisibility rule.
Step 1: Divide the number into two parts: the last two digits and the rest of the number. For 285, the last two digits are 85, and the rest is 2.
Step 2: Multiply the rest of the number by 5, i.e., 2 × 5 = 10.
Step 3: Add the result from Step 2 to the last two digits. 85 + 10 = 95.
Step 4: Check if the result from Step 3 is a multiple of 57. Since 95 is not a multiple of 57, 285 is not divisible by 57.
Tips and Tricks for Divisibility Rule of 57
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 57.
- Know the multiples of 57: Memorize the multiples of 57 (57, 114, 171, 228, etc.) to quickly check divisibility. If the result from the addition is a multiple of 57, then the number is divisible by 57.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 57. For example, check if 5706 is divisible by 57 using the divisibility test. Divide 5706 into 57 and 06. Multiply 57 by 5, i.e., 5 × 5 = 25. Add the result to 06, 06 + 25 = 31, which is small. Since 31 is not a multiple of 57, 5706 is not divisible by 57.
- 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.
Common Mistakes and How to Avoid Them in Divisibility Rule of 57
The divisibility rule of 57 helps us to quickly check if a given number is divisible by 57, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps: dividing the number into two parts, multiplying the rest by 5, and then adding it to the last two digits. Then check whether it is a multiple of 57.
Mistake 2
Including the last two digits in multiplication.
Students should keep in mind that they should exclude the last two digits while multiplying and include only the rest of the number.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number as a result. The process should be repeated until we get a result that is easy to check for divisibility by 57.
Mistake 4
Confusing the steps.
Students often confuse the steps or forget them. To avoid the error, students should practice regularly.
Divisibility Rule of 57 Examples
Problem 1
Does the number 4567 satisfy the divisibility rule of 57?
No, 4567 is not divisible by 57.
Explanation
To check if 4567 is divisible by 57, use the rule:
1) Add the last digit, 7, to five times the remaining number, 456.
2) Calculate: 5 × 456 + 7 = 2287.
3) Since 2287 is not divisible by 57, neither is 4567.
Problem 2
Check if the number 6273 is divisible by 57.
Yes, 6273 is divisible by 57.
Explanation
To verify the divisibility of 6273 by 57:
1) Add the last digit, 3, to five times the remaining number, 627.
2) Calculate: 5 × 627 + 3 = 3138.
3) Since 3138 is divisible by 57 (57 × 55 = 3138), 6273 is also divisible by 57.
Problem 3
Is -3645 divisible by 57?
No, -3645 is not divisible by 57.
Explanation
To check if -3645 is divisible by 57, ignore the negative sign:
1) Add the last digit, 5, to five times the remaining number, 364.
2) Calculate: 5 × 364 + 5 = 1825.
3) Since 1825 is not divisible by 57, neither is -3645.
Problem 4
Can 8129 be divided by 57 using the divisibility rule?
No, 8129 isn't divisible by 57.
Explanation
To determine if 8129 is divisible by 57:
1) Add the last digit, 9, to five times the remaining number, 812.
2) Calculate: 5 × 812 + 9 = 4069.
3) 4069 is not divisible by 57, so 8129 is not divisible by 57.
Problem 5
Verify if 11457 is divisible by 57.
Yes, 11457 is divisible by 57.
Explanation
To check the divisibility of 11457 by 57:
1) Add the last digit, 7, to five times the remaining number, 1145.
2) Calculate: 5 × 1145 + 7 = 5732.
3) Since 5732 is divisible by 57 (57 × 100 = 5732), 11457 is also divisible by 57.
FAQs on Divisibility Rule of 57
1.What is the divisibility rule for 57?
2. How many numbers are there between 1 and 1000 that are divisible by 57?
3.Is 114 divisible by 57?
4.What if I get 0 after adding?
5.Does the divisibility rule of 57 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 57?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 57 with numbers?
8.What role do numbers and Divisibility Rule of 57 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 57 skills?
Important Glossary for Divisibility Rule of 57
- 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 57 are 57, 114, 171, etc.
- Integer: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Addition: Addition is the process of finding the total or sum by combining two or more numbers.
- Verification: Verification is the process of checking or proving the truth or accuracy of something, such as using division to confirm divisibility.
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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.
