100 LearnersLast updated on May 26th, 2025
Factors of 309
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 309, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 309?
The numbers that divide 309 evenly are known as factors of 309.
A factor of 309 is a number that divides the number without remainder.
The factors of 309 are 1, 3, 103, and 309.
Negative factors of 309: -1, -3, -103, and -309.
Prime factors of 309: 3 and 103.
Prime factorization of 309: 3 × 103.
The sum of factors of 309: 1 + 3 + 103 + 309 = 416
How to Find Factors of 309?
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 309. Identifying the numbers which are multiplied to get the number 309 is the multiplication method.
Step 1: Multiply 309 by 1, 309 × 1 = 309.
Step 2: Check for other numbers that give 309 after multiplying
3 × 103 = 309
Therefore, the positive factor pairs of 309 are: (1, 309), (3, 103).
All these factor pairs result in 309.
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 309 by 1, 309 ÷ 1 = 309.
Step 2: Continue dividing 309 by the numbers until the remainder becomes 0.
309 ÷ 1 = 309
309 ÷ 3 = 103
Therefore, the factors of 309 are: 1, 3, 103, 309.
Prime Factors and Prime Factorization
The factors can be found by dividing them by 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 309 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
309 ÷ 3 = 103
103 ÷ 103 = 1
The prime factors of 309 are 3 and 103.
The prime factorization of 309 is: 3 × 103.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 309 is divided by 3 to get 103.
Step 2: Now divide 103 by 103 to get 1. Here, 103 is a prime number that cannot be divided anymore. So, the prime factorization of 309 is: 3 × 103.
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 309: (1, 309), (3, 103).
Negative factor pairs of 309: (-1, -309), (-3, -103).
Common Mistakes and How to Avoid Them in Factors of 309
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 309, 1 and 309 are also factors.
Factors of 309 Examples
Problem 1
There are 3 groups and 309 students. How will they divide equally?
Each group will have 103 students.
Explanation
To divide the students equally, we need to divide the total students by the number of groups.
309/3 = 103
Problem 2
A rectangular garden has a width of 3 meters, and the total area is 309 square meters. Find the length.
103 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
309 = length × 3
To find the value of length, divide 309 by 3.
309/3 = length
Length = 103.
Problem 3
There are 103 gift bags and 309 candies. How many candies will be in each bag?
Each bag will have 3 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
309/103 = 3
Problem 4
In a school, there are 309 students, and the school has 1 auditorium. How many students can sit in it?
All 309 students can sit in it.
Explanation
All students can sit in a single auditorium as there is only one group.
309/1 = 309
Problem 5
309 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 103 books.
Explanation
Divide total books by shelves.
309/3 = 103
FAQs on Factors of 309
1.What are the factors of 309?
2.Mention the prime factors of 309.
3.Is 309 a multiple of 3?
4.Mention the factor pairs of 309?
5.What is the square of 309?
6.How can children in Canada use numbers in everyday life to understand Factors of 309?
7.What are some fun ways kids in Canada can practice Factors of 309 with numbers?
8.What role do numbers and Factors of 309 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 309 skills?
Important Glossaries for Factor of 309
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 309 are 1, 3, 103, and 309.
- Prime Factors: The factors which are prime numbers. For example, 3 and 103 are prime factors of 309.
- 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 309 are (1, 309), (3, 103).
- Prime Factorization: The expression of a number as the product of its prime factors. For example, 309 can be expressed as 3 × 103.
- Multiple: A multiple is a result of multiplying a number by an integer. For example, 309 is a multiple of 3.
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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.
