125 LearnersLast updated on May 26th, 2025
Factors of 807
Factors are the numbers that divide any given number evenly without a 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 807, how they are used in real life, and tips to learn them quickly.
What are the Factors of 807?
The numbers that divide 807 evenly are known as factors of 807.
A factor of 807 is a number that divides the number without remainder.
The factors of 807 are 1, 3, 269, and 807.
Negative factors of 807: -1, -3, -269, and -807.
Prime factors of 807: 3 and 269.
Prime factorization of 807: 3 × 269.
The sum of factors of 807: 1 + 3 + 269 + 807 = 1080
How to Find Factors of 807?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 807. Identifying the numbers which are multiplied to get the number 807 is the multiplication method.
Step 1: Multiply 807 by 1, 807 × 1 = 807.
Step 2: Check for other numbers that give 807 after multiplying
3 × 269 = 807
Therefore, the positive factor pairs of 807 are: (1, 807) and (3, 269).
All these factor pairs result in 807.
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 807 by 1, 807 ÷ 1 = 807.
Step 2: Continue dividing 807 by the numbers until the remainder becomes 0.
807 ÷ 1 = 807
807 ÷ 3 = 269
Therefore, the factors of 807 are: 1, 3, 269, and 807.
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 807 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
807 ÷ 3 = 269
269 ÷ 269 = 1
The prime factors of 807 are 3 and 269.
The prime factorization of 807 is: 3 × 269.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 807 is divided by 3 to get 269.
Step 2: 269 is a prime number and cannot be divided further. So, the prime factorization of 807 is: 3 × 269.
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 807: (1, 807) and (3, 269).
Negative factor pairs of 807: (-1, -807) and (-3, -269).
Common Mistakes and How to Avoid Them in Factors of 807
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of 807, 1 and 807 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 807 consist of -1, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 2.5 is a factor because 807/2.5 = 322.8, 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 807 are prime numbers.
For example, 3 and 269 are the prime factors of 807, but it has other factors like 1, 807.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 807 as 3 × 269 and missing all the key factors.
Factors of 807 Examples
Problem 1
A group of 3 friends wants to buy 807 apples. If they want to divide them equally, how many apples will each friend get?
Each friend will get 269 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of friends.
807/3 = 269
Problem 2
A piece of land is to be divided into equal sections for 807 trees. If each section contains 1 tree, how many sections will there be?
There will be 807 sections.
Explanation
To find the number of sections, we use the number of trees per section,
807/1 = 807
Problem 3
A concert hall has 807 seats, and tickets are sold in groups of 3. How many groups are formed?
269 groups are formed.
Explanation
To find the number of groups, divide the total seats by the group size.
807/3 = 269
Problem 4
In a factory, 807 machines are placed in rows of 3. How many machines are there in each row?
There are 269 machines in each row.
Explanation
Dividing the machines by the number of rows gives the number of machines per row.
807/3 = 269
Problem 5
807 books need to be placed on 1 shelf. How many books will go on the shelf?
All 807 books will go on the shelf.
Explanation
Since there is only one shelf, all books go on it.
807/1 = 807
FAQs on Factors of 807
1.What are the factors of 807?
2.Mention the prime factors of 807.
3.Is 807 a multiple of 3?
4.Mention the factor pairs of 807?
5.What is the sum of the factors of 807?
Important Glossaries for Factor of 807
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 807 are 1, 3, 269, and 807.
- Prime factors: The factors which are prime numbers. For example, 3 and 269 are prime factors of 807.
- 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 807 are (1, 807) and (3, 269).
- Prime factorization: Breaking down a number into its prime number factors. For example, 807 = 3 × 269.
- Negative factors: Negative numbers that divide the original number without a remainder. For example, -1, -3, -269, and -807 are negative factors of 807.
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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.
