Factors of 150
Did you know, the number 150 is obtained by the product of three prime numbers and these are 2, 3, and 5? In this lesson, we will learn to calculate the factors of 150, the prime factors of 150, and the factors of 150 in pairs along with solved examples for a better understanding.
 Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150
 Prime Factorization of 150: 2 × 3 × 5^{2}
1.  What Are the Factors of 150? 
2.  How to Calculate the Factors of 150? 
3.  Factors of 150 by Prime Factorization 
4.  Factors of 150 in Pairs 
5.  Important Notes 
6.  FAQs on Factors of 150 
What Are the Factors of 150?
The factors of 150 are the numbers that on dividing 150 leave no remainder. Since 150 is a composite number, it will have more than two factors.
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
How to Calculate the Factors of 150?
Let us calculate the factors of 150.
When considering numbers that can divide 150 without remainders, we start with 1, then check 2, 3, 4, 5, 6, 7, 8, 9, etc. up to 75 (which is exactly half of 150).
Division 
Remainder 

150/1  gives remainder 0 hence, 1 is a factor 
150/2  gives remainder 0 hence, 2 is a factor 
150/3  gives remainder 0 hence, 3 is a factor 
150/5  gives remainder 0 hence, 5 is a factor 
150/6  gives remainder 0 hence, 6 is a factor 
150/10  gives remainder 0 hence, 10 is a factor 
150/15  gives remainder 0 hence, 15 is a factor 
150/25  gives remainder 0 hence, 25 is a factor 
150/30  gives remainder 0 hence, 30 is a factor 
150/50  gives remainder 0 hence, 50 is a factor 
150/75  gives remainder 0 hence, 75 is a factor 
150/150  gives remainder 0 hence, 150 is a factor 
Hence, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150.
Explore factors using illustrations and interactive examples.
 Factors of 25  The factors of 25 are 1, 5, and 25.
 Factors of 125  The factors of 125 are 1, 5, 25, and 125.
 Factors of 250  The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
 Factors of 90  The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 150 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 using the following methods.
Method 1: Division method
Now let us find the prime factors of 150 by division method.
Divide the number 150 with the smallest prime number, i.e. 2.
150/2 = 75
Again, divide 75 by 2.
75/2 = 37.5
This cannot be a factor, so moving to the next prime number.
75/3 = 25
Again, divide 25 by 3.
25/3 = 8.333
Now, if we divide 25 by 3 we get a fraction number, which cannot be a factor.
Now, proceed to the next prime numbers, i.e. 5.
25/5 = 5
Again, divide 5 by 5.
5/5 = 1
We get 1 at the end and we cannot further proceed with the division method.
So, the prime factorization of 150 is 2 x 3 x 5 x 5 = 2 x 3 × 5^{2} where 2, 3, and 5 are the prime numbers.
Method 2: Factor tree
The prime factors of 150 are: 150 = 2 x 3 x 5^{2}
Further, find the products of the multiplicands in different orders to obtain the composite factors of the number.
Thus, the factors can be written including both prime and composite numbers as 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150
Now that we have done the prime factorization of our number, we can multiply them 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 150 in Pairs
Factor Pair 
Product of Factors 

1 and 150  1 x 150 = 150 
2 and 75  2 x 75 = 150 
3 and 50  3 x 50 = 150 
5 and 30  5 x 30 = 150 
6 and 25  6 x 25 = 150 
10 and 15  10 x 15 = 150 
The product of two negative numbers is a positive number. The pair factors having negative factors are called negative pair factors.
The negative pair factors of 150 are, (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), (10, 15).
Important Notes:
 Only whole numbers and integers can be factors.
 Only composite numbers can have more than two factors.
Factors of 150 Solved Examples

Example 1: What is the sum of all the factors of the number 150, including 150?
Solution:
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The sum of all the factors will be: 1+ 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 150 = 372Thus, the sum of all the factors of 150 is 372.

Example 2: Write all the factors of 150 which are also divisible by 3.
Solution:
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
We know that the divisibility rule of 3 is that the sum of all the digits of the number must be divisible by 3.Hence, factors of 150 and multiples of 3 are 3, 6, 15, 30, 75, and 150.
FAQs on Factors of 150
What are the factors of 150?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Is 150 prime or composite?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
150 is a composite number since it has more than two factors.
Is 150 a perfect square?
A number is a perfect square if and only if its square root is an integer.
So √150 = 12.2474487, which is not an integer.
Hence, 150 is not a perfect square.
How can you represent 150 as the product of its primes?
The prime factorization of 150 is 2 × 3 × 5 × 5.
What are the common factors of 150 and 200?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.
The common factors of 150 and 200 are 1, 2, 5, 10, 25 and 50.
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