115 LearnersLast updated on May 26th, 2025
Factors of 1809
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 1809, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1809?
The numbers that divide 1809 evenly are known as factors of 1809.
A factor of 1809 is a number that divides the number without remainder.
The factors of 1809 are 1, 3, 19, 27, 57, 63, 171, 513, 603, and 1809.
Negative factors of 1809: -1, -3, -19, -27, -57, -63, -171, -513, -603, and -1809.
Prime factors of 1809: 3 and 19.
Prime factorization of 1809: 3^2 × 19 × 19.
The sum of factors of 1809: 1 + 3 + 19 + 27 + 57 + 63 + 171 + 513 + 603 + 1809 = 3266
How to Find Factors of 1809?
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 1809. Identifying the numbers which are multiplied to get the number 1809 is the multiplication method.
Step 1: Multiply 1809 by 1, 1809 × 1 = 1809.
Step 2: Check for other numbers that give 1809 after multiplying
3 × 603 = 1809
19 × 95 = 1809
27 × 67 = 1809
57 × 31 = 1809
Therefore, the positive factor pairs of 1809 are: (1, 1809), (3, 603), (19, 95), (27, 67), (57, 31).
All these factor pairs result in 1809.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 simple division method -
Step 1: Divide 1809 by 1, 1809 ÷ 1 = 1809.
Step 2: Continue dividing 1809 by the numbers until the remainder becomes 0.
1809 ÷ 1 = 1809
1809 ÷ 3 = 603
1809 ÷ 19 = 95
1809 ÷ 27 = 67
1809 ÷ 57 = 31
Therefore, the factors of 1809 are: 1, 3, 19, 27, 57, 63, 171, 513, 603, 1809.
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 1809 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
1809 ÷ 3 = 603
603 ÷ 3 = 201
201 ÷ 3 = 67
67 ÷ 67 = 1
The prime factors of 1809 are 3 and 19.
The prime factorization of 1809 is: 3^2 × 19 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1809 is divided by 3 to get 603.
Step 2: Now divide 603 by 3 to get 201.
Step 3: Then divide 201 by 3 to get 67.
Step 4: Divide 67 by 67 to get 1.
Here, 67 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1809 is: 3^2 × 19 × 19.
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 1809: (1, 1809), (3, 603), (19, 95), (27, 67), and (57, 31).
Negative factor pairs of 1809: (-1, -1809), (-3, -603), (-19, -95), (-27, -67), and (-57, -31).
Common Mistakes and How to Avoid Them in Factors of 1809
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 number. Always remember to include 1 and the number itself.
For example, in factors of 1809, 1 and 1809 are also factors.
Factors of 1809 Examples
Problem 1
There are 57 people and 1809 candies. How will they divide it equally?
They will get 31 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of people.
1809/57 = 31
Problem 2
A garden is rectangular, the length of the garden is 19 meters and the total area is 1809 square meters. Find the width.
95 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1809 = 19 × width
To find the value of width, we need to shift 19 to the left side.
1809/19 = width
Width = 95.
Problem 3
There are 27 baskets and 1809 apples. How many apples will be in each basket?
Each basket will have 67 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
1809/27 = 67
Problem 4
In a class, there are 1809 students, and 3 groups. How many students are there in each group?
There are 603 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
1809/3 = 603
Problem 5
1809 books need to be arranged in 19 shelves. How many books will go on each shelf?
Each of the shelves has 95 books.
Explanation
Divide total books with shelves.
1809/19 = 95
FAQs on Factors of 1809
1.What are the factors of 1809?
2.Mention the prime factors of 1809.
3.Is 1809 a multiple of 3?
4.Mention the factor pairs of 1809?
5.What is the square of 1809?
6.How can children in India use numbers in everyday life to understand Factors of 1809?
7.What are some fun ways kids in India can practice Factors of 1809 with numbers?
8.What role do numbers and Factors of 1809 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 1809 skills?
Important Glossaries for Factor of 1809
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1809 are 1, 3, 19, 27, 57, 63, 171, 513, 603, and 1809.
- Prime factors: The factors which are prime numbers. For example, 3 and 19 are prime factors of 1809.
- 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 1809 are (1, 1809), (3, 603), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 1809 is 3^2 × 19 × 19.
- Multiple: A product of a given number and an integer. For example, 1809 is a multiple of 3.
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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.
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