188 LearnersLast updated on May 26th, 2025
Factors Of 209
A number that can divide another number evenly without leaving any remainder is called a factor. Factors are useful in many real-life situations, such as construction, where it is used to determine the dimensions of materials to avoid waste. Next, let's discuss the factors of 209.
What are the Factors of 209?
Prime numbers can have just two factors, which are 1 and the number itself. Composite numbers have more than two factors. Now, let us learn more about the factors of 209.
Negative factors of 209: -1, -11, -19, -209
Prime factors of 209: 11 and 19
Prime factorization of 209: 11 × 19
The sum of factors of 209: 1 + 11 + 19 + 209 = 240
How to Find the Factors of 209?
For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:
- Use of Multiplication Method
- Use of Division Method
- Use of Prime Factors and Prime Factorization.
So, here we discuss a detailed explanation of the following methods:
Finding Factors Using Multiplication Method
So in the multiplication method, we will try to find out what numbers will multiply together, and give us the value 209. We will check the factors step by step:
Step 1: Start to multiply with numbers, which gives the value of 209.
Start with 1, and continue to multiply with other numbers.
1 × 209 = 209
11 × 19 = 209
Step 2: After the calculation, we get these numbers, the factors of 209.
Step 3: The positive factor pairs of 209 found through multiplication are (1, 209) and (11, 19).
Step 4: The negative factor pairs of 209 are (-1, -209) and (-11, -19).
Finding Factors Using Division Method
Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 209:
Step 1: Divide 209 by smaller numbers and see if there is any remainder. E.g., 209/1 = 209.
Step 2: We will continue in the same way and check for other numbers as well. For 209, the factors are 1, 11, 19, and 209. Because 209 can be divided evenly by these numbers.
Prime Factors and Prime Factorization
By Using Prime Factorization: When using this method, the number is divided by its prime numbers until it is completely factored.
2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.
209 ÷ 11 = 19
The prime factorization of 209 is :
209 = 11 × 19
Finally, using the prime factorization method, the prime factors of 209 are 11 and 19.
Using Factor Tree:
A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.
Step 1: 209 divided by 11 gives us the answer 19.
Step 2: Since 19 is a prime number, it cannot be divided further.
The prime factorization of 209 is written below :
209 = 11 × 19.
Factor Pairs Of 209:
Every number has either a positive or negative factor. Let us look at those sets of factors.
Positive pair Factors: (1, 209), (11, 19)
Negative pair Factors: (-1, -209), (-11, -19)
Common Mistakes and How to Avoid Them in Factors Of 209
Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
Mistake 1
Confusing Factors with Multiples
The factors can divide a number exactly, whereas multiples are the product of multiplying the number by whole numbers. For example for 12, the factors are 1, 2, 3, 4, 6, and 12. And the multiples are 12, 24, and 36, etc… To avoid this confusion, always understand the concept separately.
Factors Of 209 Examples
Problem 1
Find the lowest common multiple (LCM) and greatest common factor (GCF) of 209 and 220.
LCM of 209 and 220 is 4180, and GCF of 209 and 220 is 11.
Explanation
The LCM is the smallest multiple of a given two numbers, whereas the GCF is the largest number that can divide evenly two or more numbers. The calculations are :
Step 1: Find the prime factorization of 209 and 220
Prime factors of 209 = 11 × 19
Prime factors of 220 = 22 × 5 × 11
GCF is the lowest power of all common prime factors.
GCF = 111 = 11
LCM is the highest power of each prime factor present in both numbers.
LCM = 23 × 5 × 11× 19 = 4180.
Problem 2
If a teacher has 209 students for a group activity and wants to divide them into equal groups, with each group having the same number of students. How many students can be there in each group?
The teacher can choose 19 groups of 11 students.
Explanation
The teacher can have two possible groups of students, which is :
Step 1: Find the factors of 209
Factors of 209 = 1, 11, 19, and 209.
Step 2: The possible ways to organize the students are:
11 groups of 19 students each,
19 groups of 11 students each
If the teacher chooses 19 groups of 11 students, each group will have a balanced number of students for the activity.
Problem 3
What are the common factors of 209 and 200
Common factors of 209 and 200 = 1
Explanation
To find the common factor of 209 and 200
Step 1: List down the factors of 209 and 200
Factors of 209 = 1, 11, 19, 209.
Factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
Common factors of 209 and 200 = 1.
FAQs on Factors Of 209
1.What is the factorization method of 209?
2.Is 209 a perfect square?
3.What are the factors of 209?
4.Is 209 a divisible number?
5.Is 209 a prime or composite number?
6.How can children in Thailand use numbers in everyday life to understand Factors Of 209?
7.What are some fun ways kids in Thailand can practice Factors Of 209 with numbers?
8.What role do numbers and Factors Of 209 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors Of 209 skills?
Important Glossaries For Factors Of 209
- Factors: The factors of numbers are complete numbers, that can be divided into another number evenly without remainder. Like 6 is divisible by 1, 2, 3, and 6, therefore, 1, 2, 3, and 6 are the factors of 6.
- Prime Factors: Prime numbers that multiply together to give a certain product. For 209 the prime factors are 11 and 19.
- Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
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About BrightChamps in Thailand
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.
