123 LearnersLast updated on May 26th, 2025
Factors of 800
Factors are numbers that divide a given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally or arranging things. In this topic, we will learn about the factors of 800, how they are used in real life, and tips to learn them quickly.
What are the Factors of 800?
The numbers that divide 800 evenly are known as factors of 800.
A factor of 800 is a number that divides the number without a remainder.
The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800.
Negative factors of 800: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -160, -200, -400, and -800.
Prime factors of 800: 2 and 5.
Prime factorization of 800: 25 × 52.
The sum of factors of 800: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 80 + 100 + 160 + 200 + 400 + 800 = 2047
How to Find Factors of 800?
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 800. Identifying the numbers which are multiplied to get the number 800 is the multiplication method.
Step 1: Multiply 800 by 1, 800 × 1 = 800.
Step 2: Check for other numbers that give 800 after multiplying:
2 × 400 = 800
4 × 200 = 800
5 × 160 = 800
8 × 100 = 800
10 × 80 = 800
16 × 50 = 800
20 × 40 = 800
25 × 32 = 800
Therefore, the positive factor pairs of 800 are: (1, 800), (2, 400), (4, 200), (5, 160), (8, 100), (10, 80), (16, 50), (20, 40), (25, 32).
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 in whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 800 by 1, 800 ÷ 1 = 800.
Step 2: Continue dividing 800 by the numbers until the remainder becomes 0.
800 ÷ 1 = 800
800 ÷ 2 = 400
800 ÷ 4 = 200
800 ÷ 5 = 160
800 ÷ 8 = 100
800 ÷ 10 = 80
800 ÷ 16 = 50
800 ÷ 20 = 40
800 ÷ 25 = 32
Therefore, the factors of 800 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 800 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 800 are 2 and 5.
The prime factorization of 800 is: 25 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 800 is divided by 2 to get 400.
Step 2: Now divide 400 by 2 to get 200.
Step 3: Then divide 200 by 2 to get 100.
Step 4: Divide 100 by 2 to get 50.
Step 5: Divide 50 by 2 to get 25.
Step 6: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 800 is: 25 × 52.
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 800: (1, 800), (2, 400), (4, 200), (5, 160), (8, 100), (10, 80), (16, 50), (20, 40), (25, 32).
Negative factor pairs of 800: (-1, -800), (-2, -400), (-4, -200), (-5, -160), (-8, -100), (-10, -80), (-16, -50), (-20, -40), (-25, -32).
Common Mistakes and How to Avoid Them in Factors of 800
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 800, 1 and 800 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors.
For example, the factors of 800 include -1, -2, -4, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 800/1.5 = 533.333, 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 800 are prime numbers.
For example, 2 and 5 are the prime factors of 800, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 800 as 25 × 52 and missing all the key factors.
Factors of 800 Examples
Problem 1
A factory produces 800 widgets, and they need to be packed into boxes of 8. How many boxes are needed?
They will need 100 boxes.
Explanation
To determine how many boxes are needed, divide the total number of widgets by the number of widgets per box.
800/8 = 100
Problem 2
A piece of cloth is 800 meters long, and it's cut into pieces of 25 meters each. How many pieces can be obtained?
32 pieces.
Explanation
To find the number of pieces, divide the total length by the length of each piece.
800/25 = 32
Problem 3
A theater has 800 seats and 40 rows. How many seats are there per row?
Each row has 20 seats.
Explanation
To find the number of seats per row, divide the total number of seats by the number of rows.
800/40 = 20
Problem 4
A bank has 800 coins and needs to distribute them equally in 50 envelopes. How many coins will each envelope contain?
Each envelope will contain 16 coins.
Explanation
To find the number of coins per envelope, divide the total number of coins by the number of envelopes.
800/50 = 16
Problem 5
A library has 800 books and needs to distribute them equally across 10 shelves. How many books per shelf?
Each shelf will have 80 books.
Explanation
Divide the total books by the number of shelves.
800/10 = 80
FAQs on Factors of 800
1.What are the factors of 800?
2.Mention the prime factors of 800.
3.Is 800 a multiple of 4?
4.Mention the factor pairs of 800?
5.What is the square of 800?
6.How can children in Thailand use numbers in everyday life to understand Factors of 800?
7.What are some fun ways kids in Thailand can practice Factors of 800 with numbers?
8.What role do numbers and Factors of 800 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 800 skills?
Important Glossaries for Factors of 800
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 800.
- 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 800 are (1, 800), (2, 400), etc.
- Prime factorization: Writing a number as the product of its prime factors. For example, the prime factorization of 800 is 25 × 52.
- Multiple: A number that can be divided by another number without a remainder. For example, 800 is a multiple of 4.
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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.
