122 LearnersLast updated on May 26th, 2025
Factors of 609
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 609, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 609?
The numbers that divide 609 evenly are known as factors of 609.
A factor of 609 is a number that divides the number without remainder.
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, and 609.
Negative factors of 609: -1, -3, -7, -21, -29, -87, -203, and -609.
Prime factors of 609: 3, 7, and 29.
Prime factorization of 609: 3 × 7 × 29.
The sum of factors of 609: 1 + 3 + 7 + 21 + 29 + 87 + 203 + 609 = 960
How to Find Factors of 609?
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 609. Identifying the numbers which are multiplied to get the number 609 is the multiplication method.
Step 1: Multiply 609 by 1, 609 × 1 = 609.
Step 2: Check for other numbers that give 609 after multiplying
3 × 203 = 609
7 × 87 = 609
21 × 29 = 609
Therefore, the positive factor pairs of 609 are: (1, 609), (3, 203), (7, 87), and (21, 29). All these factor pairs result in 609. 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 609 by 1, 609 ÷ 1 = 609.
Step 2: Continue dividing 609 by the numbers until the remainder becomes 0.
609 ÷ 1 = 609
609 ÷ 3 = 203
609 ÷ 7 = 87
609 ÷ 21 = 29
Therefore, the factors of 609 are: 1, 3, 7, 21, 29, 87, 203, 609.
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 609 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
609 ÷ 3 = 203
203 ÷ 7 = 29
29 ÷ 29 = 1
The prime factors of 609 are 3, 7, and 29.
The prime factorization of 609 is: 3 × 7 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 609 is divided by 3 to get 203.
Step 2: Now divide 203 by 7 to get 29.
Step 3: Here, 29 is a prime number, that cannot be divided anymore.
So, the prime factorization of 609 is: 3 × 7 × 29.
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 609: (1, 609), (3, 203), (7, 87), and (21, 29).
Negative factor pairs of 609: (-1, -609), (-3, -203), (-7, -87), and (-21, -29).
Common Mistakes and How to Avoid Them in Factors of 609
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 609, 1 and 609 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 609 consist of -1, -3, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 609/1.5 = 406, 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 609 are prime numbers.
For example, 3, 7, and 29 are the prime factors of 609, but it has other factors like 21, 87.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 609 as 3 × 7 × 29 and missing all the key factors.
Factors of 609 Examples
Problem 1
There are 21 teams and 609 points to be distributed. How many points will each team get if distributed equally?
Each team will get 29 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
609/21 = 29
Problem 2
A garden is rectangular, the length of the garden is 7 meters and the total area is 609 square meters. Find the width.
87 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
609 = 7 × width
To find the value of width, we need to shift 7 to the left side.
609/7 = width
Width = 87.
Problem 3
There are 3 sections in a library and 609 books. How many books will be in each section?
Each section will have 203 books.
Explanation
To find the books in each section, divide the total books by the sections.
609/3 = 203
Problem 4
In a contest, there are 87 participants and 609 prizes. How many prizes will each participant receive if distributed equally?
Each participant will receive 7 prizes.
Explanation
Dividing the prizes by the total participants will get the number of prizes each participant receives.
609/87 = 7
Problem 5
609 pieces of candy need to be evenly distributed among 29 children. How many candies will each child get?
Each child will get 21 candies.
Explanation
Divide total candies by the number of children.
609/29 = 21
FAQs on Factors of 609
1.What are the factors of 609?
2.Mention the prime factors of 609.
3.Is 609 a multiple of 3?
4.Mention the factor pairs of 609?
5.What is the square of 609?
Important Glossaries for Factors of 609
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 609 are 1, 3, 7, 21, 29, 87, 203, and 609.
- Prime factors: The factors which are prime numbers. For example, 3, 7, and 29 are prime factors of 609.
- 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 609 are (1, 609), (3, 203), etc.
- Prime factorization: It is the expression of a number as a product of its prime factors. For example, the prime factorization of 609 is 3 × 7 × 29.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 609 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.
Fun Fact
: She loves to read number jokes and games.
