In Mathematics, factors of 200 are the natural numbers that can divide the original number (i.e. 200) evenly. These factors are also called divisors of 200. Since 200 is an even composite number, therefore the number of factors will be greater than two. Another definition of factors of 200 is: when the product of two natural numbers equals 200, then the numbers are the required factors. To find these factors we can use simple division methods and prime factorisation methods.
The factors of 200 can be represented in both positive and negative forms. For example, the pair factor of 200 is expressed as (1, 200) and (-1, -200). If we multiply a pair of negative numbers, such as multiplying -1 and -200, we will get the original number 200. In this article, we are going to learn what are the factors of 200, positive and negative pair factors and the prime factorisation of 200 with many solved examples.
Table of Contents:
- What are the Factors of 200?
- Pair Factors of 200
- How to Find the Factors of 200?
- Prime Factorisation of 200
- Solved Examples
- Practice Questions
- FAQs
What are the Factors of 200?
The factors of 200 are the numbers that divide the original number 200 exactly and leaves the remainder 0. As the number 200 is a composite number, it has many factors other than 1 and 200. Thus, the factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200. Similarly, the negative factors of 200 are -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 Factorisation of 200: 2 × 2 × 2 × 5 × 5 or 2^{3}×5^{2}. |
Pair Factors of 200
The pair factors of 200 are the pair of numbers that results in the original number, on multiplication.
- 1 × 200 = 200
- 2 × 100 = 200
- 4 × 50 = 200
- 5 × 40 = 200
- 8 × 25 = 200
- 10 × 20 = 200
Therefore, the positive pair factors of 200 are (1, 200), (2,100), (4,50), ( 5,40), (8,25) and (10,20).
The product of two negative pair factors will also result in the original number.
- -1 × -200 = 200
- -2 × -100 = 200
- -4 × -50 = 200
- -5 × -40 = 200
- -8 × -25 = 200
- -10 × -20 = 200
Therefore, the negative pair factors are (-1, -200), (-2, -100), (-4, -50), (-5, -40), (-8, -25), (-10, -20)
How to Find the Factors of 200?
The factors can be determined, by dividing the number by all such natural numbers, by which we get the remainder equal to zero.
Division Method |
200 ÷ 1 = 200 |
200 ÷ 2 = 100 |
200 ÷ 4 = 50 |
200 ÷ 5 = 40 |
200 ÷ 8 = 25 |
200 ÷ 10 = 20 |
200 ÷ 20 = 10 |
200 ÷ 25 = 8 |
200 ÷ 40 = 5 |
200 ÷ 50 = 4 |
200 ÷ 100 = 2 |
200 ÷ 200 = 1 |
Therefore, we can conclude the factors of 200, i.e., 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
More Factors
Prime Factorisation of 200
If we prime factorise 200, we will get the prime numbers that divide the original number, evenly. Also, we can represent 200 in prime factor form.
In this method, we start dividing the number, starting with the smallest prime number and continue the division till we get 1.
Dividing 200 by smallest prime number | 200 ÷ 2 = 100 |
100 divided by 2 | 100 ÷ 2 = 50 |
50 divided by 2 | 50 ÷ 2 = 25 |
25 is divisible by prime number 5 | 25 ÷ 5 = 5 |
5 divided by 5 | 5 ÷ 5 = 1 |
Therefore, the prime factors of 200 are 2 and 5
Therefore, the Prime factorisation of 200 = 2 x 2 x 2 x 5 x 5 or 2^{3} × 5^{2}.
Solved Examples
Q.1: What is the sum of all the factors of 200?
Solution: The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
Sum = 1+ 2 + 4 + 5 + 8 + 10 + 20 + 25 + 50 + 100 + 200 = 425
Therefore, the required sum is 425.
Q.2: What is the greatest common factor of 250 and 200?
Solution: Let us list the factors of both the numbers 250 and 200.
200 → 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200
250 → 1, 2, 5, 10, 25, 50, 125, 250
Therefore, the greatest common factor of 200 and 250 is 50.
Q.3: Find the common factors of 100 and 200.
Solution: The factors are:
100 → 1, 2, 4, 5, 10, 20, 25, 50, 100
200 → 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200
Therefore, the common factors of 100 and 200 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
Practice Questions
- Find the average value of factors of 200.
- Find the common factors of 200 and 150.
- Determine if 20 is a factor of 200.
- Write the factors of 200 in product form.
- What is the HCF of 200 and 240?
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Frequently Asked Questions on Factors of 200
What are the factors of 200?
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
What is the prime factor form of 200?
The prime factor form of 200 is given by: 2 x 2 x 2 x 5 x 5.
What are the multiples of 200?
It is very easy to remember the multiples of 200 if we know the table of 2. These multiples are: 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000 and so on.
Which is the greatest factor of 200?
200 itself is the greatest factor of 200. Since 200 divided by 200 is equal to 1.
What is the GCF of 10 and 200?
The GCF of 10 and 200 is 10 only since 10 is itself a factor of 200.
Is 200 a composite number?
Yes, 200 is a composite number, because it has factors, more than two.