Factors of 300
Did you know that the number 300 is an even composite number obtained by the product of three prime numbers 2, 3, and 5? In this lesson, we will calculate the factors of 300, the prime factors of 300, and the factors of 300 in pairs along with solved examples for a better understanding.
 Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300
 Prime Factorization of 300: 300 = 2^{2} × 3 × 5^{2}
1.  What Are the Factors of 300? 
2.  How to Calculate Factors of 300? 
3.  Factors of 300 by Prime Factorization 
4.  Factors of 300 in Pairs 
5.  FAQs on Factors of 300 
What Are the Factors of 300?
The factors of 300 will be any number which on dividing 300 leaves no remainder. Since 300 is a composite number, it will have more than two factors. 300 has a total of 18 factors.
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
How to Calculate the Factors of 300?
We can calculate the factors of 300 by the division method. In this method, we divide the number by all possible numbers that can divide it completely.
In considering numbers that can divide 300 without remainders, we start with 1, then check 2, 3,.. up to 150 (which is exactly half of 300).
Numbers dividing 300  Factors of 300 

300/1 = 300  Gives remainder 0. Hence, 1 is a factor. 
300/2 = 150  Gives remainder 0. Hence, 2 is a factor. 
300/3 = 100  Gives remainder 0. Hence, 3 is a factor. 
300/4 = 75  Gives remainder 0. Hence, 4 is a factor. 
300/5 = 60  Gives remainder 0. Hence, 5 is a factor. 
300/6 = 50  Gives remainder 0. Hence, 6 is a factor. 
300/10 = 30  Gives remainder 0. Hence, 10 is a factor. 
300/12 = 25  Gives remainder 0. Hence, 12 is a factor. 
300/15 = 20  Gives remainder 0. Hence, 12 is a factor. 
300/20 = 15  Gives remainder 0. Hence, 20 is a factor. 
300/25 = 12  Gives remainder 0. Hence, 25 is a factor. 
300/30 = 10  Gives remainder 0. Hence, 30 is a factor. 
300/50 = 6  Gives remainder 0. Hence, 50 is a factor. 
300/60 = 5  Gives remainder 0. Hence, 60 is a factor. 
300/75 = 4  Gives remainder 0. Hence, 75 is a factor. 
300/100 = 3  Gives remainder 0. Hence, 100 is a factor. 
300/300 = 1  Gives remainder 0. Hence, 300 is a factor. 
Hence, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
Explore factors using illustrations and interactive examples
 Factors of 75  The factors of 75 are 1, 3, 5, 15, 25, and 75.
 Factors of 450  The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
 Factors of 360  The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
 Factors of 150  The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
 Factors of 50  The factors of 50 are 1, 2, 5, 10, 25, and 50.
 Factors of 25  The factors of 25 are 1, 5, and 25.
Tips and Tricks:
 Prime factorization of 300 = 2 × 2 × 3 × 5 × 5 = 2^{2} × 3 × 5^{2}
 To get the total numbers of factors of 300:
 Add one to the exponent of 2, 1, and 5 and multiply their sums.
 (2 + 1) × (1 + 1) × (2 + 1) = 3 × 2 × 3 = 18
 Thus, 300 has 18 factors and are as follows: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
Factors of 300 by Prime Factorization
Prime factorization of a number refers to representing a number in the form of the product of its prime factors. Prime factors of any number can be found out by the following methods:
Method 1: Division method
Let us find the prime factors of 300 by the division method.
First divide the number 300 with the smallest prime number, i.e. 2.
300/2 = 150
Again, divide 150 by 2.
150/2 = 75
2 cannot be a factor in this case, so let's consider the next prime number which can completely divide 75, i.e. 3.
75/3 = 25
Now moving to the next prime number which can completely divide 25, i.e. 5.
25/5 = 5
Again, divide 5 by 5.
5/5 = 1
We have received 1 at the end and we cannot proceed further with the division method.
Thus, the prime factorization of 300 is 2 × 2 × 3 × 5 × 5 = 2^{2} × 3 × 5^{2} where 2, 3, and 5 are the prime numbers.
Method 2: Factor tree
A factor tree is a special branching diagram where we find the factors of the given number stepbystep, then the factors of those resultant numbers, until we cannot factor them further. At the end of the branches of the factortree, we get all the prime factors of the original number.
Hence, the prime factorization of 300 is written as 2 × 2 × 3 × 5 × 5 or 2^{2 }× 3 × 5^{2}
Now that we have done the prime factorization of 300, we can multiply the numbers and get the other factors. Can you try and find out if all the factors are covered or not?
And as you might have already guessed, for prime numbers, there are no other factors.
Factors of 300 in Pairs
Pair factors of the number 300 are the whole numbers which give the original number, i.e. 300, when they are multiplied. Pair factors could be either positive or negative but never a fraction or decimal number.
There are 18 pair factors of 300. The positive pair factors of 300 are as follows:
Product of Numbers  Positive Pair Factors 

1 × 300 = 300  (1, 300) 
2 × 150 = 300  (2, 150) 
3 × 100 = 300  (3, 100) 
4 × 75 = 300  (4, 75) 
5 × 60 = 300  (5, 60) 
6 × 50 = 300  (6, 50) 
10 × 30 = 300  (10, 30) 
12 × 25 = 300  (12, 25) 
15 × 20 = 300  (15, 20) 
The negative pair factors of 300 are as follows:
Product of Numbers  Negative Pair Factors 

1 × 300 = 300  (1, 300) 
2 × 150 = 300  (2, 150) 
3 × 100 = 300  (3, 100) 
4 × 75 = 300  (4, 75) 
5 × 60 = 300  (5, 60) 
6 × 50 = 300  (6, 50) 
10 × 30 = 300  (10, 30) 
12 × 25 = 300  (12, 25) 
15 × 20 = 300  (15, 20) 
Important Notes:
 Only whole numbers and integers can be converted to factors.
 Only composite numbers can have more than two factors.
 Every factor of a given number is either less than or equal to the given number.
Factors of 300 Solved Examples

Example 1: Can you help James find out if 15 is a factor of 300 or not?
Solution:
Factors of 300 will be the numbers that can totally divide 300 and leave no remainder.
So, 300/15 = 20
Here, 15 completely divides 300.Hence, 15 is a factor of 300.

Example 2: Write all the factors of 300 which are also the factors of 450.
Solution:
Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
And factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450Hence, the common factors of 300 and 450 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
FAQs on Factors of 300
What are the factors 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.
What are the factor pairs of 300?
Pair factors of the number 300 are the whole numbers which give the original number, i.e. 300, when they are multiplied.
Pair factors could be either positive or negative but not a fraction or decimal number.
There are 18 pair factors of 300 and they are as follows:
Positive pair factors of 300 are (1, 300), (2, 150), (3, 100), (4, 75), (5, 60), (6, 50), (10, 30), (12, 25), and (15, 20).
Negative pair factors of 300 are (1, 300), (2, 150), (3, 100), (4, 75), (5, 60), (6, 50), (10, 30), (12, 25), and (15, 20).
Is 300 divisible by a perfect square?
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
Among the factors of 300, the numbers 1, 25, and 100 are perfect squares. Hence, 300 is divisible by a perfect square.
What is the HCF of 300 and 450?
Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 450 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
Thus, HCF of 300 and 450 is 150.
What are the common factors of 300 and 360?
Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The common factors of 300 and 360 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
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