103 LearnersLast updated on May 26th, 2025
Factors of 12800
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 12800, how they are used in real life, and tips to learn them quickly.
What are the Factors of 12800?
The numbers that divide 12800 evenly are known as factors of 12800.
A factor of 12800 is a number that divides the number without remainder.
The factors of 12800 include 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 2560, 3200, 6400, and 12800.
Negative factors of 12800: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -128, -160, -200, -256, -320, -400, -640, -800, -1280, -1600, -2560, -3200, -6400, and -12800.
Prime factors of 12800: 2 and 5.
Prime factorization of 12800: 2^8 × 5^2.
The sum of factors of 12800: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 64 + 80 + 100 + 128 + 160 + 200 + 256 + 320 + 400 + 640 + 800 + 1280 + 1600 + 2560 + 3200 + 6400 + 12800 = 31911.
How to Find Factors of 12800?
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 12800. Identifying the numbers which are multiplied to get the number 12800 is the multiplication method.
Step 1: Multiply 12800 by 1, 12800 × 1 = 12800.
Step 2: Check for other numbers that give 12800 after multiplying
2 × 6400 = 12800
4 × 3200 = 12800
5 × 2560 = 12800
8 × 1600 = 12800
10 × 1280 = 12800
16 × 800 = 12800
20 × 640 = 12800
25 × 512 = 12800
32 × 400 = 12800
40 × 320 = 12800
50 × 256 = 12800
64 × 200 = 12800
80 × 160 = 12800
100 × 128 = 12800
Therefore, the positive factor pairs of 12800 are: (1, 12800), (2, 6400), (4, 3200), (5, 2560), (8, 1600), (10, 1280), (16, 800), (20, 640), (25, 512), (32, 400), (40, 320), (50, 256), (64, 200), (80, 160), (100, 128). All these factor pairs result in 12800.
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 12800 by 1, 12800 ÷ 1 = 12800.
Step 2: Continue dividing 12800 by the numbers until the remainder becomes 0.
12800 ÷ 1 = 12800
12800 ÷ 2 = 6400
12800 ÷ 4 = 3200
12800 ÷ 5 = 2560
12800 ÷ 8 = 1600
12800 ÷ 10 = 1280
12800 ÷ 16 = 800
12800 ÷ 20 = 640
12800 ÷ 25 = 512
12800 ÷ 32 = 400
12800 ÷ 40 = 320
12800 ÷ 50 = 256
12800 ÷ 64 = 200
12800 ÷ 80 = 160
12800 ÷ 100 = 128
Therefore, the factors of 12800 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 2560, 3200, 6400, and 12800.
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 12800 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
12800 ÷ 2 = 6400
6400 ÷ 2 = 3200
3200 ÷ 2 = 1600
1600 ÷ 2 = 800
800 ÷ 2 = 400
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 5 = 10
10 ÷ 5 = 2
2 ÷ 2 = 1
The prime factors of 12800 are 2 and 5.
The prime factorization of 12800 is: 2^8 × 5^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 12800 is divided by 2 to get 6400.
Step 2: Now divide 6400 by 2 to get 3200.
Step 3: Then divide 3200 by 2 to get 1600.
Step 4: Divide 1600 by 2 to get 800.
Step 5: Divide 800 by 2 to get 400.
Step 6: Divide 400 by 2 to get 200.
Step 7: Divide 200 by 2 to get 100.
Step 8: Divide 100 by 2 to get 50.
Step 9: Divide 50 by 5 to get 10.
Step 10: Divide 10 by 5 to get 2.
Here, 2 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 12800 is: 2^8 × 5^2.
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 12800: (1, 12800), (2, 6400), (4, 3200), (5, 2560), (8, 1600), (10, 1280), (16, 800), (20, 640), (25, 512), (32, 400), (40, 320), (50, 256), (64, 200), (80, 160), (100, 128).
Negative factor pairs of 12800: (-1, -12800), (-2, -6400), (-4, -3200), (-5, -2560), (-8, -1600), (-10, -1280), (-16, -800), (-20, -640), (-25, -512), (-32, -400), (-40, -320), (-50, -256), (-64, -200), (-80, -160), (-100, -128).
Common Mistakes and How to Avoid Them in Factors of 12800
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 word. Always remember to include 1 and the number itself.
For example, in factors of 12800, 1 and 12800 is also a factor.
Factors of 12800 Examples
Problem 1
A bakery has 12800 cookies to be packed in boxes. If each box holds 100 cookies, how many boxes are needed?
128 boxes are needed.
Explanation
To find the number of boxes needed, divide the total cookies by the number of cookies per box.
12800/100 = 128
Problem 2
A factory produces 12800 units of a product and wants to distribute them into 64 equal shipments. How many units will each shipment contain?
Each shipment will contain 200 units.
Explanation
To find the units in each shipment, divide the total units by the number of shipments.
12800/64 = 200
Problem 3
There are 12800 apples in an orchard, and they need to be placed in crates of 400 apples each. How many crates are required?
32 crates are required.
Explanation
To find the number of crates required, divide the total apples by the number of apples per crate.
12800/400 = 32
Problem 4
A publishing house has 12800 pages to print, divided among 320 books. How many pages will each book contain?
Each book will contain 40 pages.
Explanation
Dividing the total pages by the number of books gives the number of pages per book.
12800/320 = 40
Problem 5
A company has 12800 units of product and wants to store them in two warehouses equally. How many units will each warehouse hold?
Each warehouse will hold 6400 units.
Explanation
Divide the total units by the number of warehouses.
12800/2 = 6400
FAQs on Factors of 12800
1.What are the factors of 12800?
2.Mention the prime factors of 12800.
3.Is 12800 a multiple of 128?
4.Mention the factor pairs of 12800?
5.What is the square of 12800?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 12800?
7.What are some fun ways kids in Bahrain can practice Factors of 12800 with numbers?
8.What role do numbers and Factors of 12800 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 12800 skills?
Important Glossaries for Factor of 12800
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 12800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 256, 320, 400, 640, 800, 1280, 1600, 2560, 3200, 6400, and 12800.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 12800.
- 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 12800 are (1, 12800), (2, 6400), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 12800 is 2^8 × 5^2.
- Multiple: A number that can be divided by another number without a remainder. For example, 12800 is a multiple of 128.
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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
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