126 LearnersLast updated on May 26th, 2025
Factors of 509
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 509, their use in real life, and tips to learn them quickly.
What are the Factors of 509?
The numbers that divide 509 evenly are known as factors of 509.
A factor of 509 is a number that divides the number without a remainder.
The factors of 509 are 1 and 509.
Negative factors of 509: -1 and -509.
Prime factors of 509: 7 and 73.
Prime factorization of 509: 7 × 73.
The sum of factors of 509: 1 + 509 = 510
How to Find Factors of 509?
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 509. Identifying the numbers which are multiplied to get the number 509 is the multiplication method.
Step 1: Multiply 509 by 1, 509 × 1 = 509.
Step 2: Since 509 is a product of prime numbers, check for combinations: 7 × 73 = 509
Therefore, the positive factor pairs of 509 are: (1, 509) and (7, 73). All these factor pairs result in 509.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 509 by 1, 509 ÷ 1 = 509.
Step 2: Continue dividing 509 by numbers until the remainder becomes 0.
509 ÷ 1 = 509
509 ÷ 7 = 73
Therefore, the factors of 509 are: 1, 7, 73, and 509.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 509 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
509 ÷ 7 = 73
73 ÷ 73 = 1
The prime factors of 509 are 7 and 73.
The prime factorization of 509 is: 7 × 73.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 509 is divided by 7 to get 73.
Step 2: Now divide 73 by 73 to get 1. Here, 73 is a prime number and cannot be divided further.
So, the prime factorization of 509 is: 7 × 73.
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 509: (1, 509), (7, 73).
Negative factor pairs of 509: (-1, -509), (-7, -73).
Common Mistakes and How to Avoid Them in Factors of 509
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 the factors for every word. Always remember to include 1 and the number itself.
For example, in factors of 509, 1 and 509 are also factors.
Mistake 2
Missing Negative Factors
We are often used to mentioning only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 509 include -1 and -509.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 509/1.5 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, 7 and 73 are the prime factors of 509, but it also has the factor 509 itself.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 509 as 7 × 73 and missing key factors.
Factors of 509 Examples
Problem 1
There are 509 people attending a concert and 7 buses. How many people will be in each bus?
Each bus will hold 73 people.
Explanation
To divide the people equally, we need to divide the total number of people by the number of buses.
509 ÷ 7 = 73
Problem 2
A rectangular yard has a length of 73 meters, and the total area is 509 square meters. Find the width.
7 meters.
Explanation
To find the width of the yard, we use the formula, Area = length × width
509 = 73 × width
To find the value of width, we need to shift 73 to the left side.
509 ÷ 73 = width
Width = 7.
Problem 3
A library has 509 books and 1 shelf. How many books will be on the shelf?
There will be 509 books on the shelf.
Explanation
To find how many books will be on the shelf, divide the total number of books by 1.
509 ÷ 1 = 509
Problem 4
509 marbles need to be arranged in 7 boxes. How many marbles will go in each box?
Each box will have 73 marbles.
Explanation
Dividing the marbles by the number of boxes gives the number of marbles in each box.
509 ÷ 7 = 73
Problem 5
If there are 509 cans and 73 boxes, how many cans will be in each box?
Each box will have 7 cans.
Explanation
Divide the total cans by the number of boxes.
509 ÷ 73 = 7
FAQs on Factors of 509
1.What are the factors of 509?
2.Mention the prime factors of 509.
3.Is 509 a multiple of 7?
4.Mention the factor pairs of 509?
5.What is the square of 509?
6.How can children in Canada use numbers in everyday life to understand Factors of 509?
7.What are some fun ways kids in Canada can practice Factors of 509 with numbers?
8.What role do numbers and Factors of 509 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 509 skills?
Important Glossaries for Factor of 509
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 509 are 1, 7, 73, and 509.
- Prime factors: The factors which are prime numbers. For example, 7 and 73 are prime factors of 509.
- 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 509 are (1, 509) and (7, 73).
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 509 is 7 × 73.
- Negative factors: The negative counterparts of the positive factors. For example, -1 and -509 are negative factors of 509.
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About BrightChamps in Canada
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.
