Factors of 200

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.

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.

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.

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 2³ × 5².

Video Lesson on Prime Factors

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 + 40 + 50 + 100 + 200 = 465

Therefore, the required sum is 465.

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

1. Find the average value of factors of 200.
2. Find the common factors of 200 and 150.
3. Determine if 20 is a factor of 200.
4. Write the factors of 200 in product form.
5. What is the HCF of 200 and 240?

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