What are the Factors of 300?
If the number 300 is divided by a natural number such that the remainder is zero, the natural number is known as a factor of 300. Here, the quotient obtained on division is also a factor of 300.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300 because all these numbers divide the number 300 evenly.
List of the Factors of 300
Divisibility rules and division facts can be applied to determine the factors of 300.
For 20 we can see that the factor pairs start to repeat so we can stop checking at this step.
So, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
[Note: If we divide 300 by 21, we get the quotient and remainder as 14 and 6, respectively. So, 21 is not a factor of 300. Similarly, you can check for other numbers as well.]
The Prime Factorization of 300
If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the prime factors of that natural number. The process of writing this multiplication of prime factors is known as prime factorization.
The prime factorization of 300 can be represented by using a factor tree as shown below.
So, the prime factorization of 300 is 300 = 2 x 2 x 3 x 5 x 5 and the prime factors of 300 are 2, 3, and 5.
Factor Pairs of 300
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 300
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Rapid Recall
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
Solved Factors of 300 Examples
Example 1: Find the highest common factor of 300 and 120.
Solution:
Prime factorization of 300 = 2 x 2 x 3 x 5 x 5.
Prime factorization of 120 = 2 x 2 x 2 x 3 x 5
So, the common factors of 300 and 120 are 2, 2, 3 and 5.
Multiply them to get highest common factor 2 x 2 x 3 x 5 = 60
Therefore, the highest common factor of 300 and 120 is 60.
Example 2: Find the common factors of 300 and 200.
Solution:
Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300
Factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.
Therefore, the common factors of 300 and 200 are 1, 2, 4, 5, 10, 20, 25, 50 and 100.
Example 3: James has to plant 300 plants on the ground in rows. He wants to put the same number of plants in each row without any plants remaining. Should he plant 20, 21 or 22 in each row?
Solution:
To get an equal number of plants in each row, we will check whether any of 20,21 or 22 is a factor of 300 because factors divide a number completely without leaving a remainder.
As we know the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
As 20 among 20, 21 and 22 is a factor of 300.
So, James should arrange 20 plants in each row so that there are no plants remaining.
300 ÷ 16 = 18 R12 Here the remainder is 12 which means 16 is not a factor of 300.
A number which has only two factors, that is, 1 and the number itself is called a prime number.
Composite numbers are numbers that have more than two factors.
The prime factors of 300 are 2, 3, and 5.
A number which divides the given number evenly is called a factor of the given number.