Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 509 people attending a concert and 7 buses. How many people will be in each bus?
Each bus will hold 73 people.
To divide the people equally, we need to divide the total number of people by the number of buses.
509 ÷ 7 = 73
A rectangular yard has a length of 73 meters, and the total area is 509 square meters. Find the width.
7 meters.
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.
A library has 509 books and 1 shelf. How many books will be on the shelf?
There will be 509 books on the shelf.
To find how many books will be on the shelf, divide the total number of books by 1.
509 ÷ 1 = 509
509 marbles need to be arranged in 7 boxes. How many marbles will go in each box?
Each box will have 73 marbles.
Dividing the marbles by the number of boxes gives the number of marbles in each box.
509 ÷ 7 = 73
If there are 509 cans and 73 boxes, how many cans will be in each box?
Each box will have 7 cans.
Divide the total cans by the number of boxes.
509 ÷ 73 = 7
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.
: She loves to read number jokes and games.