Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and ways to avoid them.
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.
To determine how many boxes are needed, divide the total number of widgets by the number of widgets per box.
800/8 = 100
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.
To find the number of pieces, divide the total length by the length of each piece.
800/25 = 32
A theater has 800 seats and 40 rows. How many seats are there per row?
Each row has 20 seats.
To find the number of seats per row, divide the total number of seats by the number of rows.
800/40 = 20
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.
To find the number of coins per envelope, divide the total number of coins by the number of envelopes.
800/50 = 16
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.
Divide the total books by the number of shelves.
800/10 = 80
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.
: She loves to read number jokes and games.