122 LearnersLast updated on May 26th, 2025
Factors of -200
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 -200, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -200?
The numbers that divide -200 evenly are known as factors of -200.
A factor of -200 is a number that divides the number without a remainder.
The factors of -200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
Negative factors of -200: -1, -2, -4, -5, -8, -10, -20, -25, -40, -50, -100, and -200. Prime factors of -200: 2 and 5.
Prime factorization of -200: -1 × 2^3 × 5^2.
The sum of factors of 200 (ignoring signs): 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 40 + 50 + 100 + 200 = 465
How to Find Factors of -200?
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 -200. Identifying the numbers which are multiplied to get the number -200 is the multiplication method.
Step 1: Multiply -200 by 1, -200 × 1 = -200.
Step 2: Check for other numbers that give -200 after multiplying 2
× -100 = -200
4 × -50 = -200
5 × -40 = -200
8 × -25 = -200
10 × -20 = -200
Therefore, the positive factor pairs of -200 are: (1, -200), (2, -100), (4, -50), (5, -40), (8, -25), (10, -20).
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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide -200 by 1, -200 ÷ 1 = -200.
Step 2: Continue dividing -200 by the numbers until the remainder becomes
0. -200 ÷ 1 = -200
-200 ÷ 2 = -100
-200 ÷ 4 = -50
-200 ÷ 5 = -40
-200 ÷ 8 = -25
-200 ÷ 10 = -20
Therefore, the factors of -200 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
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 -200 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-200 ÷ -1 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of -200 are 2 and 5.
The prime factorization of -200 is: -1 × 2^3 × 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, -200 is divided by -1 to get 200.
Step 2: Now divide 200 by 2 to get 100.
Step 3: Then divide 100 by 2 to get 50.
Step 4: Divide 50 by 2 to get 25.
Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -200 is: -1 × 23 × 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 -200: (1, -200), (2, -100), (4, -50), (5, -40), (8, -25), and (10, -20).
Negative factor pairs of -200: (-1, 200), (-2, 100), (-4, 50), (-5, 40), (-8, 25), and (-10, 20).
Common Mistakes and How to Avoid Them in Factors of -200
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 -200, 1 and -200 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 -200 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 -200/1.5 = -133.333, 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 -200 are prime numbers.
For example, 2 and 5 are the prime factors of -200, 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 -200 as -1 × 2^3 × 5^2 and missing all the key factors.
Factors of -200 Examples
Problem 1
A company has 200 units of products and wants to distribute them in equal parts among 10 departments. How many units will each department get?
Each department will get 20 units.
Explanation
To divide the products equally, we need to divide the total products by the number of departments.
200/10 = 20
Problem 2
A rectangular garden has a width of 10 meters and a total area of 200 square meters. What is the length of the garden?
20 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
200 = length × 10
To find the value of length, we need to shift 10 to the left side.
200/10 = length Length = 20.
Problem 3
A construction project requires 5 workers to pour 200 cubic meters of concrete. How much concrete will each worker pour?
Each worker will pour 40 cubic meters of concrete.
Explanation
To find the concrete each worker will handle, divide the total concrete by the number of workers.
200/5 = 40
Problem 4
If a school has 8 classes and 200 students, how many students are there in each class?
There are 25 students in each class.
Explanation
Dividing the students by the number of classes, we will get the number of students in each class.
200/8 = 25
Problem 5
A library has 200 books to be organized in 5 sections. How many books will go in each section?
Each section will have 40 books.
Explanation
Divide the total books by sections.
200/5 = 40
FAQs on Factors of -200
1.What are the factors of -200?
2.Mention the prime factors of -200.
3.Is 200 a multiple of 8?
4.Mention the factor pairs of -200?
5.What is the square of 200?
Important Glossaries for Factor of -200
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -4, etc., are negative factors of -200.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of -200.
- 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 -200 are (1, -200), (2, -100), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of -200 is -1 × 2^3 × 5^2.
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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.
