119 LearnersLast updated on May 26th, 2025
Divisibility Rule of 51
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 51.
What is the Divisibility Rule of 51?
The divisibility rule for 51 is a method by which we can determine if a number is divisible by 51 without using the division method. Check whether 408 is divisible by 51 using the divisibility rule.
Step 1: Check if the number is divisible by both 3 and 17, as 51 is the product of these two numbers.
- To check for divisibility by 3: Sum the digits of the number. If the sum is divisible by 3, then the number is divisible by 3. In 408, the sum of the digits is 4+0+8=12, which is divisible by 3.
- To check for divisibility by 17: Divide the number by 17 to see if it results in a whole number. Here, 408 ÷ 17 = 24, which is a whole number.
Since 408 is divisible by both 3 and 17, it is also divisible by 51.
Tips and Tricks for Divisibility Rule of 51
Learning divisibility rules will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 51.
- Know the multiples of 51: Memorize the multiples of 51 (51, 102, 153, 204, etc.) to quickly check divisibility. If a number is a multiple of 51, then it is divisible by 51.
- Use divisibility rules of factors: Apply the divisibility rules of 3 and 17 (since 51=3×17) to determine divisibility by 51.
- Repeat the process for large numbers: Break down large numbers using divisibility by 3 and 17. For example, check if 867 is divisible by 51. First, sum the digits: 8+6+7=21 (divisible by 3). Then, divide 867 by 17. If it results in a whole number (867 ÷ 17 = 51), then it is divisible by 51.
- Use the division method to verify: Students can use the division method to verify and cross-check their results. This will help them confirm their findings and improve their understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 51
The divisibility rule of 51 helps us quickly check if a given number is divisible by 51, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking both divisibility rules.
Ensure to check divisibility by both 3 and 17, as 51 is the product of these numbers.
Mistake 2
Incorrectly summing digits for divisibility by 3.
Carefully add the digits to determine if the sum is divisible by 3.
Mistake 3
Skipping the division for 17.
Always divide the number by 17 to ensure it results in a whole number.
Mistake 4
Assuming divisibility by one factor is sufficient.
Remember, a number must be divisible by both 3 and 17 to be divisible by 51.
Mistake 5
Confusing the steps.
Practice regularly to familiarize yourself with the process and avoid confusion.
Divisibility Rule of 51 Examples
Problem 1
Is 561 divisible by 51?
Yes, 561 is divisible by 51.
Explanation
To check if 561 is divisible by 51, we can use the divisibility rule for 51.
1) Multiply the last digit of the number by 5, 1 × 5 = 5.
2) Subtract the result from the remaining digits, excluding the last digit, 56 – 5 = 51.
3) Check if the result is a multiple of 51. Yes, 51 is a multiple of 51 (51 × 1 = 51).
Problem 2
Check the divisibility rule of 51 for 102.
Yes, 102 is divisible by 51.
Explanation
For checking the divisibility rule of 51 for 102,
1) Multiply the last digit of the number by 5, 2 × 5 = 10.
2) Subtract the result from the remaining digits, excluding the last digit, 10 – 10 = 0.
3) The result is 0, which indicates that 102 is divisible by 51.
Problem 3
Is 408 not divisible by 51?
No, 408 is not divisible by 51.
Explanation
To verify if 408 is divisible by 51, we follow the steps:
1) Multiply the last digit of the number by 5, 8 × 5 = 40.
2) Subtract the result from the remaining digits, excluding the last digit, 40 – 40 = 0.
3) Check if the result is a multiple of 51. No, 0 is not a multiple of 51.
Problem 4
Can 255 be divisible by 51 following the divisibility rule?
No, 255 isn't divisible by 51.
Explanation
To check if 255 is divisible by 51, we follow these steps:
1) Multiply the last digit of the number by 5, 5 × 5 = 25.
2) Subtract the result from the remaining digits, excluding the last digit, 25 – 25 = 0.
3) Check if the result is a multiple of 51. No, 0 isn't a multiple of 51.
Problem 5
Check the divisibility rule of 51 for 204.
Yes, 204 is divisible by 51.
Explanation
To determine if 204 is divisible by 51, follow these steps:
1) Multiply the last digit of the number by 5, 4 × 5 = 20.
2) Subtract the result from the remaining digits, excluding the last digit, 20 – 20 = 0.
3) The result is 0, indicating that 204 is divisible by 51.
FAQs on Divisibility Rule of 51
1.What is the divisibility rule for 51?
2.How many numbers are there between 1 and 100 that are divisible by 51?
3.Is 204 divisible by 51?
4.What if a number is divisible by 3 but not by 17?
5.Does the divisibility rule of 51 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 51?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 51 with numbers?
8.What role do numbers and Divisibility Rule of 51 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 51 skills?
Important Glossary for Divisibility Rule of 51
- Divisibility rule: A set of rules used to determine whether a number is divisible by another number without performing division.
- Multiple: A result obtained by multiplying a number by an integer. For example, multiples of 51 are 51, 102, 153, etc.
- Integer: Numbers that include all whole numbers, negative numbers, and zero.
- Sum of digits: The result of adding together the digits of a number, used to determine divisibility by 3.
- Whole number: A number without fractions; an integer.
Explore More numbers
About BrightChamps in United Kingdom
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.
