120 LearnersLast updated on May 26th, 2025
Factors of 802
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 802, how they are used in real life, and tips to learn them quickly.
What are the Factors of 802?
The numbers that divide 802 evenly are known as factors of 802.
A factor of 802 is a number that divides the number without remainder.
The factors of 802 are 1, 2, 401, and 802.
Negative factors of 802: -1, -2, -401, and -802.
Prime factors of 802: 2 and 401.
Prime factorization of 802: 2 × 401.
The sum of factors of 802: 1 + 2 + 401 + 802 = 1206
How to Find Factors of 802?
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 802. Identifying the numbers which are multiplied to get the number 802 is the multiplication method.
Step 1: Multiply 802 by 1, 802 × 1 = 802.
Step 2: Check for other numbers that give 802 after multiplying
2 × 401 = 802
Therefore, the positive factor pairs of 802 are: (1, 802) and (2, 401).
All these factor pairs result in 802.
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 as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 802 by 1, 802 ÷ 1 = 802.
Step 2: Continue dividing 802 by the numbers until the remainder becomes 0.
802 ÷ 1 = 802
802 ÷ 2 = 401
Therefore, the factors of 802 are: 1, 2, 401, 802.
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 802 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
802 ÷ 2 = 401
401 ÷ 401 = 1
The prime factors of 802 are 2 and 401.
The prime factorization of 802 is: 2 × 401.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 802 is divided by 2 to get 401.
Step 2: Now divide 401 by 401 to get 1. Here, 401 is a prime number that cannot be divided anymore. So, the prime factorization of 802 is: 2 × 401.
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 802: (1, 802) and (2, 401).
Negative factor pairs of 802: (-1, -802) and (-2, -401).
Common Mistakes and How to Avoid Them in Factors of 802
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 802, 1 and 802 are also factors.
Mistake 2
Missing Negative Factors
We often only mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 802 consist of -1, -2, -401, etc.
Mistake 3
Including Fractions
Children might sometimes include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 802/1.5 = 534.666, 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 802 are prime numbers. While 2 and 401 are the prime factors of 802, it has other factors like 1, 802.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 802 as 2 × 401 and missing key factors.
Factors of 802 Examples
Problem 1
A company has 4 departments and 802 files. How will they distribute them equally?
Each department will get 200 files.
Explanation
To distribute the files equally, we need to divide the total files by the number of departments. 802/4 = 200.5 (Since 4 is not a factor of 802, files cannot be distributed equally without splitting files.)
Problem 2
A rectangular billboard has a length of 2 meters and a total area of 802 square meters. Find the width.
401 meters.
Explanation
To find the width of the billboard, we use the formula, Area = length × width
802 = 2 × width
To find the value of width, we need to shift 2 to the left side.
802/2 = width
Width = 401.
Problem 3
There are 802 pages in a book and 2 sections. How many pages are in each section?
Each section will have 401 pages.
Explanation
To find the pages in each section, divide the total pages by the number of sections.
802/2 = 401
Problem 4
A conference has 802 attendees and 2 seating areas. How many attendees will be in each area?
There are 401 attendees in each seating area.
Explanation
Dividing the attendees by the total seating areas, we will get the number of attendees in each area.
802/2 = 401
Problem 5
802 plants need to be arranged in 2 gardens. How many plants will go in each garden?
Each of the gardens has 401 plants.
Explanation
Divide total plants by gardens.
802/2 = 401
FAQs on Factors of 802
1.What are the factors of 802?
2.Mention the prime factors of 802.
3.Is 802 a multiple of 4?
4.Mention the factor pairs of 802?
5.What is the square of 802?
Important Glossaries for Factors of 802
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 802 are 1, 2, 401, and 802.
- Prime factors: The factors which are prime numbers. For example, 2 and 401 are prime factors of 802.
- 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 802 are (1, 802) and (2, 401).
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 802 is 2 × 401.
- Multiplication method: A method used to find factors by identifying pairs of numbers that result in the original number when multiplied together. For example, using the multiplication method to find factors of 802 results in pairs (1, 802) and (2, 401).
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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.
