Factors of 200 Using Prime Factorization
What are the Factors of 200?
If the number 200 is divided by a natural number such that the remainder is zero, then this natural number is known as a factor of 200.
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200 because all these numbers divide the number 200 evenly.
The quotient obtained on dividing a number by its factor is also a factor of that number.
List of the Factors of 200
Divisibility rules and division facts are applied to determine the factors of 200.
If we continue checking for numbers greater than 10 we will notice that the factor pairs start to repeat. Hence, we can stop checking at this step.
So, the factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
[Note: If we divide 200 by 11, we get the quotient and remainder as 18 and 2, respectively. So, 11 is not a factor of 200. Similarly, you can check for other numbers as well.]
Prime Factorization of 200
Numbers, especially composite numbers, can be expressed as a product of prime numbers. These prime numbers are known as the prime factors of that number. The process of writing this multiplication of prime factors is known as prime factorization.
The prime factorization of 200 can be represented by using a factor tree as shown below.
So, the prime factorization of 200 is 200 = 2 \(\times \) 2 \(\times \) 2 \(\times \) 5 \(\times \) 5 and the prime factors of 200 are 2 and 5.
Factor Pairs of 200
A factor pair of a number is a set of any of its two factors such that their product is the number itself. A factor pair can be negative or positive.
Positive Factor Pairs of 200
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Rapid Recall
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
Solved Factors of 200 Examples
Example 1: Annie has four children. She wants to distribute 200 dollars among them as pocket money so that each of them will get an equal amount. How much money will each child get?
Solution:
Number of children = 4
Total amount = 200 dollars
To distribute an equal amount, divide 200 by 4, that is,
\(\frac{200}{4} \)
= \(\frac{50~\times~4}{4} \) [(50, 4) is a factor pair of 200]
= \(50 \) [Divide numerator and denominator by 4]
Therefore, each child will get 50 dollars.
Example 2: Find the highest common factor of 200 and 150.
Solution:
Prime factors of 200 = 2, 2, 2, 5 and 5.
Prime factors of 150 = 2, 3, 5 and 5
So, the common factors of 200 and 150 are 2, 5 and 5.
Multiply them to get highest common factor 2 \(\times\) 5 \(\times\) 5 = 50
Therefore, the highest common factor of 200 and 150 is 50.
Example 3: Find the common factors of 200 and 125.
Solution:
Factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
Factors of 125 = 1, 5, 25 and 125.
Therefore, the common factors of 200 and 150 are 1, 5 and 25.
200 \(\div\) 40 = 5 R0
Here the remainder is 0 which shows us that 40 is a factor of 200.
As per definition, prime numbers have only two factors, that is,1 and the number itself. But factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200. Here the number of factors are more than two, so 200 is not a prime number.
Composite numbers are numbers that have more than two factors.
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
When we divide 200 by 7 we get 28 as the quotient and 4 as the remainder, that is, the remainder is not zero. In other words, 200 is not evenly divisible by 7. Hence, 7 is not a factor of 200.