123 LearnersLast updated on May 26th, 2025
Factors of 820
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 820, how they are used in real life, and tips to learn them quickly.
What are the Factors of 820?
The numbers that divide 820 evenly are known as factors of 820.
A factor of 820 is a number that divides the number without a remainder.
The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820.
Negative factors of 820: -1, -2, -4, -5, -10, -20, -41, -82, -164, -205, -410, and -820.
Prime factors of 820: 2, 5, and 41.
Prime factorization of 820: (22 times 5 times 41).
The sum of factors of 820: 1 + 2 + 4 + 5 + 10 + 20 + 41 + 82 + 164 + 205 + 410 + 820 = 1764
How to Find Factors of 820?
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 820. Identifying the numbers which are multiplied to get the number 820 is the multiplication method.
Step 1: Multiply 820 by 1, 820 × 1 = 820.
Step 2: Check for other numbers that give 820 after multiplying
2 × 410 = 820
4 × 205 = 820
5 × 164 = 820
10 × 82 = 820
20 × 41 = 820
Therefore, the positive factor pairs of 820 are: (1, 820), (2, 410), (4, 205), (5, 164), (10, 82), (20, 41). 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 820 by 1, 820 ÷ 1 = 820.
Step 2: Continue dividing 820 by the numbers until the remainder becomes 0.
820 ÷ 1 = 820
820 ÷ 2 = 410
820 ÷ 4 = 205
820 ÷ 5 = 164
820 ÷ 10 = 82
820 ÷ 20 = 41
Therefore, the factors of 820 are: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820.
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 820 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
820 ÷ 2 = 410
410 ÷ 2 = 205
205 ÷ 5 = 41
41 ÷ 41 = 1
The prime factors of 820 are 2, 5, and 41.
The prime factorization of 820 is: (22 times 5 times 41).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 820 is divided by 2 to get 410.
Step 2: Now divide 410 by 2 to get 205.
Step 3: Then divide 205 by 5 to get 41. Here, 41 is a prime number, which cannot be divided anymore. So, the prime factorization of 820 is: (22 times 5 times 41).
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 820: (1, 820), (2, 410), (4, 205), (5, 164), (10, 82), and (20, 41).
Negative factor pairs of 820: (-1, -820), (-2, -410), (-4, -205), (-5, -164), (-10, -82), and (-20, -41).
Common Mistakes and How to Avoid Them in Factors of 820
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 820, 1 and 820 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 820 consist of -1, -2, -4, 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 820/1.5 = 546.666..., 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 820 are prime numbers.
For example, 2, 5, and 41 are the prime factors of 820, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 820 as (22 times 5 times 41) and missing all the key factors.
Factors of 820 Examples
Problem 1
There are 41 students and 820 pencils. How will they distribute them equally?
Each student will get 20 pencils.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of students.
820/41 = 20
Problem 2
An auditorium has 205 chairs arranged in rows. The total capacity is 820 people. How many rows are there?
4 rows.
Explanation
To find the number of rows, use the formula, Capacity = rows × chairs per row
820 = rows × 205
To find the number of rows, divide the total capacity by chairs per row.
820/205 = 4
Problem 3
There are 10 teams and 820 points available. How many points will each team get if divided equally?
Each team will get 82 points.
Explanation
To find the points each team will receive, divide the total points by the number of teams.
820/10 = 82
Problem 4
A company has 820 tasks to complete and 5 departments. How many tasks will each department have?
Each department will have 164 tasks.
Explanation
Dividing the tasks by the total departments, we will get the number of tasks per department.
820/5 = 164
Problem 5
820 books need to be placed in 2 libraries. How many books will each library receive?
Each library will have 410 books.
Explanation
Divide the total books by the number of libraries.
820/2 = 410
FAQs on Factors of 820
1.What are the factors of 820?
2.Mention the prime factors of 820.
3.Is 820 a multiple of 4?
4.Mention the factor pairs of 820?
5.What is the square of 820?
6.How can children in United States use numbers in everyday life to understand Factors of 820?
7.What are some fun ways kids in United States can practice Factors of 820 with numbers?
8.What role do numbers and Factors of 820 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 820 skills?
Important Glossaries for Factor of 820
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 41 are prime factors of 820.
- 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 820 are (1, 820), (2, 410), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 820 is (22 times 5 times 41).
- Negative factors: The negative counterparts of the positive factors. For example, -1, -2, -4, etc., are negative factors of 820.
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About BrightChamps in United States
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.
