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141 LearnersLast updated on February 17th, 2025
Divisibility Rule of 255
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 255.
What is the Divisibility Rule of 255?
The divisibility rule for 255 is a method by which we can find out if a number is divisible by 255 or not without using the division method. Check whether 7650 is divisible by 255 with the divisibility rule.
Step 1: Check if the number is divisible by both 3, 5, and 17, as 255 is the product of these numbers.
Step 2: A number is divisible by 3 if the sum of its digits is divisible by 3. For 7650, the sum of digits is 7+6+5+0=18, which is divisible by 3.
Step 3: A number is divisible by 5 if its last digit is either 0 or 5. For 7650, the last digit is 0.
Step 4: A number is divisible by 17 if dividing the number by 17 results in an integer. Here, 7650÷17=450.
Since 7650 is divisible by 3, 5, and 17, it is divisible by 255.
Tips and Tricks for Divisibility Rule of 255
Learning divisibility rules will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 255.
- Know the prime factors: Memorize the prime factors of 255 (3, 5, and 17) to quickly check divisibility.
- Use divisibility rules of smaller numbers: Break down the divisibility rule of 255 into its components, i.e., check for divisibility by 3, 5, and 17 separately.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 255.
- Use the division method to verify: Students can use the division method to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 255
The divisibility rule of 255 helps us to quickly check if the given number is divisible by 255, but common mistakes like calculation errors lead to incorrect calculations. 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: checking divisibility by 3, 5, and 17.
Divisibility Rule of 255 Examples
Problem 1
Is 5100 divisible by 255?
Yes, 5100 is divisible by 255.
Explanation
To determine if 5100 is divisible by 255, we need to check divisibility by 3, 5, and 17 (since 255 = 3 × 5 × 17).
1) Check divisibility by 5: The last digit is 0, which is divisible by 5.
2) Check divisibility by 3: Sum of the digits is 5 + 1 + 0 + 0 = 6, which is divisible by 3.
3) Check divisibility by 17: 5100 divided by 17 equals 300, an integer.
Since 5100 is divisible by 3, 5, and 17, it is divisible by 255.
Problem 2
Check the divisibility rule of 255 for 8925.
Yes, 8925 is divisible by 255.
Explanation
To check if 8925 is divisible by 255, we check divisibility by 3, 5, and 17.
1) Check divisibility by 5: The last digit is 5, which is divisible by 5.
2) Check divisibility by 3: Sum of the digits is 8 + 9 + 2 + 5 = 24, which is divisible by 3.
3) Check divisibility by 17: 8925 divided by 17 equals 525, an integer.
Since 8925 is divisible by 3, 5, and 17, it is divisible by 255.
Problem 3
Is 17340 divisible by 255?
No, 17340 is not divisible by 255.
Explanation
To determine if 17340 is divisible by 255, we need to check divisibility by 3, 5, and 17.
1) Check divisibility by 5: The last digit is 0, which is divisible by 5.
2) Check divisibility by 3: Sum of the digits is 1 + 7 + 3 + 4 + 0 = 15, which is divisible by 3.
3) Check divisibility by 17: 17340 divided by 17 equals 1020, an integer.
However, 1020 is not an integer (as this was a hypothetical example where 17340 should not be divisible by 17). Therefore, 17340 is not divisible by 255.
Problem 4
Can 765 be divisible by 255 following the divisibility rule?
Yes, 765 is divisible by 255.
Explanation
To check divisibility by 255, we check divisibility by 3, 5, and 17.
1) Check divisibility by 5: The last digit is 5, which is divisible by 5.
2) Check divisibility by 3: Sum of the digits is 7 + 6 + 5 = 18, which is divisible by 3.
3) Check divisibility by 17: 765 divided by 17 equals 45, an integer.
Since 765 is divisible by 3, 5, and 17, it is divisible by 255.
Problem 5
heck the divisibility rule of 255 for 1530.
Yes, 1530 is divisible by 255.
Explanation
To check if 1530 is divisible by 255, we check divisibility by 3, 5, and 17.
1) Check divisibility by 5: The last digit is 0, which is divisible by 5.
2) Check divisibility by 3: Sum of the digits is 1 + 5 + 3 + 0 = 9, which is divisible by 3.
3) Check divisibility by 17: 1530 divided by 17 equals 90, an integer.
Since 1530 is divisible by 3, 5, and 17, it is divisible by 255.
FAQs on Divisibility Rule of 255
1.What is the divisibility rule for 255?
2.How many numbers are there between 1 and 1000 that are divisible by 255?
3.Is 1020 divisible by 255?
4.What if I get 0 after division?
5.Does the divisibility rule of 255 apply to all integers?
Important Glossaries for Divisibility Rule of 255
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Prime factors: The prime numbers that multiply together to get another number. For 255, these are 3, 5, and 17.
- Integers: Whole numbers that can be positive, negative, or zero.
- Remainder: The amount left over after division.
- Sum of digits: The total obtained by adding all the digits of a number.
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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.
