127 LearnersLast updated on May 26th, 2025
Factors of 204
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 204, how they are used in real life, and tips to learn them quickly.
What are the Factors of 204?
The numbers that divide 204 evenly are known as factors of 204. A factor of 204 is a number that divides the number without remainder.
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.
Negative factors of 204: -1, -2, -3, -4, -6, -12, -17, -34, -51, -68, -102, and -204.
Prime factors of 204: 2, 3, and 17.
Prime factorization of 204: 2 × 2 × 3 × 17 or 2² × 3 × 17.
The sum of factors of 204: 1 + 2 + 3 + 4 + 6 + 12 + 17 + 34 + 51 + 68 + 102 + 204 = 504
How to Find Factors of 204?
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 204. Identifying the numbers which are multiplied to get the number 204 is the multiplication method.
Step 1: Multiply 204 by 1, 204 × 1 = 204.
Step 2: Check for other numbers that give 204 after multiplying
2 × 102 = 204
3 × 68 = 204
4 × 51 = 204
6 × 34 = 204
12 × 17 = 204
Therefore, the positive factor pairs of 204 are: (1, 204), (2, 102), (3, 68), (4, 51), (6, 34), and (12, 17).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
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 204 by 1, 204 ÷ 1 = 204.
Step 2: Continue dividing 204 by the numbers until the remainder becomes 0.
204 ÷ 1 = 204
204 ÷ 2 = 102
204 ÷ 3 = 68
204 ÷ 4 = 51
204 ÷ 6 = 34
204 ÷ 12 = 17
Therefore, the factors of 204 are: 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204.
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 204 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
204 ÷ 2 = 102
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 204 are 2, 3, and 17.
The prime factorization of 204 is: 2² × 3 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 204 is divided by 2 to get 102.
Step 2: Now divide 102 by 2 to get 51.
Step 3: Then divide 51 by 3 to get 17.
Here, 17 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 204 is: 2² × 3 × 17.
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 204: (1, 204), (2, 102), (3, 68), (4, 51), (6, 34), and (12, 17).
Negative factor pairs of 204: (-1, -204), (-2, -102), (-3, -68), (-4, -51), (-6, -34), and (-12, -17).
Common Mistakes and How to Avoid Them in Factors of 204
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 204, 1 and 204 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 204 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 204/1.5 = 136, 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 204 are prime numbers. For example, 2, 3, and 17 are the prime factors of 204, but it has other factors like 6, 51.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 204 as 2² × 3 × 17 and missing all the key factors.
Factors of 204 Examples
Problem 1
There are 6 students and 204 pages to read. How will they divide the pages equally?
They will read 34 pages each.
Explanation
To divide the pages equally, we need to divide the total pages with the number of students.
204/6 = 34
Problem 2
A rectangular garden has a perimeter of 204 meters, with the length being 51 meters. Find the width.
The width is 51 meters.
Explanation
To find the width of the garden, we use the formula,
Perimeter = 2 × (length + width)
204 = 2 × (51 + width)
Solving for width, we find: 51 + width = 102
width = 51
Problem 3
There are 12 boxes and 204 toys. How many toys will be in each box?
Each box will have 17 toys.
Explanation
To find the toys in each box, divide the total toys by the number of boxes.
204/12 = 17
Problem 4
In a school, there are 204 students and 17 classes. How many students are there in each class?
There are 12 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
204/17 = 12
Problem 5
204 books need to be arranged in 34 shelves. How many books will go on each shelf?
Each shelf has 6 books.
Explanation
Divide total books by the number of shelves.
204/34 = 6
FAQs on Factors of 204
1.What are the factors of 204?
2.Mention the prime factors of 204.
3.Is 204 a multiple of 6?
4.Mention the factor pairs of 204?
5.What is the square of 204?
Important Glossaries for Factors of 204
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, and 204.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 204.
- 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 204 are (1, 204), (2, 102), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 204 is 2² × 3 × 17.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 204 is a multiple of 6.
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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.
