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Factors of 200

Factors of 200 are the numbers that multiplying two natural numbers give the result 200. There are a total 12 factors of 200 which can be negative as well as positive. Did you know that in 200BC the building of The Great Wall of China was begun? In this lesson, we will calculate the factors of 200, its prime factors, and its factors in pairs along with solved examples for a better understanding.

Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
Factors of -200: -1,- 2, -4, -5, -8, -10, - 20, -25, -40, -50, -100, and -200.
Prime Factorization of 200: 200 = 2³ × 5²

1.	What are Factors of 200?
2.	How to Calculate Factors of 200?
3.	Factors of 200 by Prime Factorization
4.	Tips and Tricks
5.	Factors of 200 in Pairs
6.	Important Notes
7.	FAQs on Factors of 200

What are Factors of 200?

One of the easiest ways to find out all the factors is to list all the possible pairs of numbers which can give you the product as 200. Here are all the possible pairs of numbers:

(1,200), (2,100), (4,50), (5,40), (8,25), (10,20)

Therefore, the factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200. Which means the number 200 is an even composite number.

How to Calculate Factors of 200?

Let us find out the factors of 200 by prime factorization method. Using the prime factorization method for 200, we will get 2 × 2 × 2 × 5 × 5 = 200. Also, we know all the factors of 200 from the discussion above.
We can observe that only 2 and 5 are the prime numbers in the factors of 200, so 2 and 5 will be the only prime factors of 200. Explore factors using illustrations and interactive examples:

Factors of 121- The factors of 121 are 1, 11, 121
Factors of 125- The factors of 125 are 1, 5, 25, 125
Factors of 128- The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
Factors of 112- The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factors of 512 - The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
Factors of 20 - The factors of 1, 2, 4, 5, 10, 20

Factors of 200 by Prime Factorization

Factors of a number are the exact divisor of the number leaving the remainder as 0.
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.

Let us understand this by prime factorization:

prime factorization of 200

Tips and Tricks

To find factors, we can apply divisibility rules.
Numbers greater than half of a given number (except the number itself) cannot be the factors of the given number.
The number of factors of a number is finite.

Factors of 200 in Pairs

Number	Pair Factors
200	(1, 200), (2,100), (4,50), ( 5,40), (8,25), (10,20)

Since the product of two negative numbers is positive, The negative factor pairs of 200 are (-1, -200), (-2, -100), (-4, -50), (-5, -40), (-8, -25), (-10, -20).

Important Notes:

Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
Decimal numbers and fractions are not considered as factors of a number.
Since 200 is an even number, it will definitely have 2 as its factor.

Example 1: One carton can hold up to 50 eggs. If Lilly has ordered 200 eggs, how many cartons will be needed to deliver all the 200 eggs together?

Solution:

From the question, we know that a carton can hold up to 50 eggs, and Lilly has ordered 200 eggs. Now, using the concept of factors and multiples, we know that 50 is one of the factors of 200. So, 200 is clearly divisible by 50.
On dividing 200 by 50, we get the answer as 4. Hence, Lilly will get all the eggs in a total of 4 cartons.
Example 2:

Steve has decided to donate 200 lunch boxes to the kids of a school. If one classroom has 40 students, in how many classrooms will Steve be able to distribute all these 200 lunch boxes?

Solution:
- Total number of lunch boxes = 200
- Students in one classroom = 40
Here, if you notice properly, you will get that 40 is one of the factors of 200. That means you can directly divide 200 by 40, and you will get a proper whole number and not a decimal number as the result.
On successful division, i.e., 200 ÷ 40, we get the answer as 5. Hence, Steve will be able to distribute these lunch boxes in 5 classrooms.
Example 3: Help Mike list out the common factors of 200 and 40.

Solution:
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
- Factors of 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
Common factors of 200 and 40 are 1, 2, 4, 5, 8, 10, 20, 40

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FAQs on Factors of 200

What are the Positive Pair Factors of 200?

The positive pair factors of 200 are (1, 200), (2,100), (4,50), ( 5,40), (8,25), and (10,20).

What are the Prime Factors of 200?

As we use prime factorization for 200, we get 2 × 2 × 2 × 5 × 5 = 200. So, the only prime factors of 200 are 2 and 5.

What are all the Factors of 200?

Factors of 200 are 1,2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.

What are the Negative Pair Factors of 200?

The negative factor pairs of 200 are (-1, -200), (-2, -100), (-4, -50), (-5, -40), (-8, -25), and (-10, -20).

How many Factors of 200 are there?

Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200. Therefore, the total factors of 200 are 12.

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