Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 6 students and 204 pages to read. How will they divide the pages equally?
They will read 34 pages each.
To divide the pages equally, we need to divide the total pages with the number of students.
204/6 = 34
A rectangular garden has a perimeter of 204 meters, with the length being 51 meters. Find the width.
The width is 51 meters.
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
There are 12 boxes and 204 toys. How many toys will be in each box?
Each box will have 17 toys.
To find the toys in each box, divide the total toys by the number of boxes.
204/12 = 17
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.
Dividing the students by the total classes, we will get the number of students in each class.
204/17 = 12
204 books need to be arranged in 34 shelves. How many books will go on each shelf?
Each shelf has 6 books.
Divide total books by the number of shelves.
204/34 = 6
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.
: She loves to read number jokes and games.