121 LearnersLast updated on May 26th, 2025
Factors of 804
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 804, how they are used in real life, and tips to learn them quickly.
What are the Factors of 804?
The numbers that divide 804 evenly are known as factors of 804.
A factor of 804 is a number that divides the number without remainder.
The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, and 804.
Negative factors of 804: -1, -2, -3, -4, -6, -12, -67, -134, -201, -268, -402, and -804.
Prime factors of 804: 2, 3, and 67.
Prime factorization of 804: 22 × 3 × 67.
The sum of factors of 804: 1 + 2 + 3 + 4 + 6 + 12 + 67 + 134 + 201 + 268 + 402 + 804 = 1904
How to Find Factors of 804?
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 804. Identifying the numbers which are multiplied to get the number 804 is the multiplication method.
Step 1: Multiply 804 by 1, 804 × 1 = 804.
Step 2: Check for other numbers that give 804 after multiplying
2 × 402 = 804
3 × 268 = 804
4 × 201 = 804
6 × 134 = 804
12 × 67 = 804
Therefore, the positive factor pairs of 804 are: (1, 804), (2, 402), (3, 268), (4, 201), (6, 134), (12, 67).
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 804 by 1, 804 ÷ 1 = 804.
Step 2: Continue dividing 804 by the numbers until the remainder becomes 0.
804 ÷ 1 = 804
804 ÷ 2 = 402
804 ÷ 3 = 268
804 ÷ 4 = 201
804 ÷ 6 = 134
804 ÷ 12 = 67
Therefore, the factors of 804 are: 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 804 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
804 ÷ 2 = 402
402 ÷ 2 = 201
201 ÷ 3 = 67
67 ÷ 67 = 1
The prime factors of 804 are 2, 3, and 67.
The prime factorization of 804 is: 22 × 3 × 67.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 804 is divided by 2 to get 402.
Step 2: Now divide 402 by 2 to get 201.
Step 3: Then divide 201 by 3 to get 67. 67 is a prime number that cannot be divided further. So, the prime factorization of 804 is: 2^2 × 3 × 67.
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 804: (1, 804), (2, 402), (3, 268), (4, 201), (6, 134), and (12, 67).
Negative factor pairs of 804: (-1, -804), (-2, -402), (-3, -268), (-4, -201), (-6, -134), and (-12, -67).
Common Mistakes and How to Avoid Them in Factors of 804
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 804, 1 and 804 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 804 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 804/1.5 = 536, 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 804 are prime numbers.
For example, 2, 3, and 67 are the prime factors of 804, but it has other factors like 4, 6, and 12.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 804 as 22 × 3 × 67 and missing all the key factors.
Factors of 804 Examples
Problem 1
A baker has 804 cupcakes and needs to pack them into boxes of 12. How many boxes are needed?
67 boxes are needed.
Explanation
To find the number of boxes, we divide the total cupcakes by the number of cupcakes per box.
804/12 = 67
Problem 2
A rectangular garden has an area of 804 square meters and a width of 4 meters. What is the garden's length?
201 meters.
Explanation
To find the length of the garden, we use the formula: Area = length × width
804 = length × 4
To find the value of length, we divide by the width.
804/4 = length
Length = 201 meters.
Problem 3
There are 134 chairs and 804 tables. How many tables will each chair have?
Each chair will have 6 tables.
Explanation
To find the tables per chair, divide the total tables by the number of chairs.
804/134 = 6
Problem 4
A library has 804 books and 6 shelves. How many books will go on each shelf?
Each shelf will have 134 books.
Explanation
Divide the total books by the number of shelves to find the number of books on each shelf.
804/6 = 134
Problem 5
A factory produces 402 gadgets every day. If they work for 2 days, how many gadgets will they produce?
They will produce 804 gadgets.
Explanation
Multiply the daily production by the number of days to find the total production.
402 × 2 = 804
FAQs on Factors of 804
1.What are the factors of 804?
2.Mention the prime factors of 804.
3.Is 804 a multiple of 3?
4.Mention the factor pairs of 804?
5.What is the square of 804?
6.How can children in Australia use numbers in everyday life to understand Factors of 804?
7.What are some fun ways kids in Australia can practice Factors of 804 with numbers?
8.What role do numbers and Factors of 804 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 804 skills?
Important Glossaries for Factor of 804
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, and 804.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 67 are prime factors of 804.
- 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 804 are (1, 804), (2, 402), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 804 is 22 × 3 × 67.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 804 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
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