120 LearnersLast updated on May 26th, 2025
Factors of 510
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 510, how they are used in real life, and tips to learn them quickly.
What are the Factors of 510?
The numbers that divide 510 evenly are known as factors of 510.
A factor of 510 is a number that divides the number without remainder.
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, and 510.
Negative factors of 510: -1, -2, -3, -5, -6, -10, -15, -17, -30, -34, -51, -85, -102, -170, -255, and -510.
Prime factors of 510: 2, 3, 5, and 17.
Prime factorization of 510: 2 × 3 × 5 × 17.
The sum of factors of 510: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 17 + 30 + 34 + 51 + 85 + 102 + 170 + 255 + 510 = 1286
How to Find Factors of 510?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 510. Identifying the numbers which are multiplied to get the number 510 is the multiplication method.
Step 1: Multiply 510 by 1, 510 × 1 = 510.
Step 2: Check for other numbers that give 510 after multiplying: 2 × 255 = 510
3 × 170 = 510
5 × 102 = 510
6 × 85 = 510
10 × 51 = 510
15 × 34 = 510
17 × 30 = 510
Therefore, the positive factor pairs of 510 are: (1, 510), (2, 255), (3, 170), (5, 102), (6, 85), (10, 51), (15, 34), (17, 30).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 510 by 1, 510 ÷ 1 = 510.
Step 2: Continue dividing 510 by the numbers until the remainder becomes 0. 510 ÷ 1 = 510
510 ÷ 2 = 255
510 ÷ 3 = 170
510 ÷ 5 = 102
510 ÷ 6 = 85
510 ÷ 10 = 51
510 ÷ 15 = 34
510 ÷ 17 = 30
Therefore, the factors of 510 are: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 510 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
510 ÷ 2 = 255
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
The prime factors of 510 are 2, 3, 5, and 17.
The prime factorization of 510 is: 2 × 3 × 5 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 510 is divided by 2 to get 255.
Step 2: Now divide 255 by 3 to get 85.
Step 3: Then divide 85 by 5 to get 17. Here, 17 is a prime number and cannot be divided anymore.
So, the prime factorization of 510 is: 2 × 3 × 5 × 17.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 510: (1, 510), (2, 255), (3, 170), (5, 102), (6, 85), (10, 51), (15, 34), (17, 30).
Negative factor pairs of 510: (-1, -510), (-2, -255), (-3, -170), (-5, -102), (-6, -85), (-10, -51), (-15, -34), (-17, -30).
Common Mistakes and How to Avoid Them in Factors of 510
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 510, 1 and 510 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 510 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 510/1.5 = 340, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 510 are prime numbers.
For example, 2, 3, 5, and 17 are the prime factors of 510, but it has other factors like 6, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 510 as 2 × 3 × 5 × 17 and missing all the key factors.
Factors of 510 Examples
Problem 1
There are 10 teams and 510 participants. How many participants will each team have?
Each team will have 51 participants.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
510/10 = 51
Problem 2
A concert hall has a rectangular stage with a length of 15 meters and a total area of 510 square meters. Find the width of the stage.
34 meters.
Explanation
To find the width of the stage, we use the formula, Area = length × width
510 = 15 × width
To find the value of width, we need to shift 15 to the left side.
510/15 = width
Width = 34.
Problem 3
There are 34 buses and 510 passengers. How many passengers will be in each bus?
Each bus will have 15 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the number of buses.
510/34 = 15
Problem 4
In a school, there are 510 students and 17 classes. How many students are there in each class?
There are 30 students in each class.
Explanation
Dividing the students by the total classes will give the number of students in each class.
510/17 = 30
Problem 5
510 books need to be arranged on 6 shelves. How many books will go on each shelf?
Each of the shelves has 85 books.
Explanation
Divide total books by shelves.
510/6 = 85
FAQs on Factors of 510
1.What are the factors of 510?
2.Mention the prime factors of 510.
3.Is 510 a multiple of 17?
4.Mention the factor pairs of 510.
5.What is the square of 510?
Important Glossaries for Factors of 510
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, and 510.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 17 are prime factors of 510.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 510 are (1, 510), (2, 255), etc.
- Multiples: A multiple is the result of multiplying a number by an integer. For example, 510 is a multiple of 17.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 510 is 2 × 3 × 5 × 17.
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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.
