Factors of 150

Factors of 150 are all the integers (both positive and negative whole numbers) that can be equally splitted into 150 and can be expressed as individual factors or factor pairs. Hence, factors of 150 can be represented in both ways.  

In this article, we will discuss how to find the factors of 150 using factor pairs and prime factorization methods.

Factors Of 

    150

Factor Pairs of 150

Factor pairs of 150 are the numbers which when multiplied in pairs obtains the result 150. To find the factors pairs of 150, we will multiply the two numbers which give us the result 150.

Example:

If 150 × 1 = 150, then (1,150) are the factor pairs of 150.

Similarly:

• 2 and 75 are factors pairs of 150 as 2 × 75 = 150

• 3 and 50 are factor pairs of 150 as  3 × 50 = 150

• 5 and 30 are factors pairs of 150 as 5 × 30 = 150

• 6 and 25 are factors pairs of 150 as 6 × 25 = 150

• 10 and 15 are factors pairs of 150 as 10 × 15 = 150

Hence, the positive pair factors of 150 are (2,75), (3,50), (5,30), (6,25), (10,15). 

Similarly, we can find the negative pair factors of 150 as shown below:

If -150 × ( -1 )= 150, then (-1,-150) are the pair factors of 150.

Similarly:

• -2 and -75 are factors pairs of 150 as (-2 × (-75)) = 150

• -3 and -50 are factor pairs of 150 as  (-3 × (- 50)) = 150

• -5 and - 30 are factors pairs of 150 as (-5 × (-30)) = 150

• - 6 and - 25 are factors pairs of 150 as (6 × (-25)) = 150

• -10 and -15 are factors pairs of 150 as (-10 × (-15))= 150

Therefore, the negative pair factors of 150 are as follows:

• (-2,-75)

•  (-3,-50)

•  (-5,-30)

• (-6,-25)

• (-10,-15)

Prime Factorization of 150

In Number theory, the prime factorization of a number 150 is the set consisting of prime numbers whose product is 150. Hence the prime factorization of 150 is 2 × 3 × 5 × 5 or 2 × 3 × 5².

What is the Prime Factorization of 150? 

150 = 2  × 3 × 5  × 5 or 2 × 3 × 5².

How to Find Prime Factorization of 150?

To find the prime factorization of 150, we will start dividing the number 150 by 2 which leaves us with the remainder 75. We can observe that the number 75 is not divisible by 2, and thus look for the next integer that the number is divisible, which happens to be 3. We then divide 75 by 3 which leaves us with the remainder 25. Again, we can observe that the number 25 is not divisible by 3, and hence look for the next integer that the number is divisible by, which happens to be 5. We then divide 25 by 5, which leaves us with the remainder 5. We observe that the number 5 is still divisible by 5, so we divide 5 by 5, which will leave us with the remainder of 1.

Therefore, 150 = 2  × 3 × 5  × 5 or 2 × 3 × 5².

All Factors of 150

All factors of 150 are the numbers that on dividing 150 obtains the remainder 0. As the number 150 is a composite number, it will have more than 2 factors.

Therefore, all factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

What are Common Factors?

Common factors are defined as the numbers that are common to two or more numbers. To find the common factor of two numbers, we will list out the factors of two numbers separately and then compare them. Now, write the factors which are common to both the numbers. These factors are known as the common factors of two numbers.

Let us understand with an example:

What is The Common Factor of 150 and 250?

Let us find the factors of 150 and 200 separately to find the common factors between them.

All Factors of 150 :  1, 2, 3, 5, 6, 10, 15, 25, 30, 50,  75, and  150.

All Factors of 200 :  1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200

Hence, the common factors of 150 and 200 are 2, 5, 10, 25, and 50.

Solved Examples

1. What is the Sum of all the Factors of 150 Excluding 150?

Solution:

As we know,

All factors of 150 : 1, 2, 3, 5, 6,10, 15, 25, 30, 50, 75, and 150

Therefore,

The sum of all the factors of 150 excluding150 is 1 + 2  + 3 + 5 + 6 + 10 + 15 + 25 +30 + 50 + 75 = 222

2. Write all the Factors of 150 Which are also a Multiple of 5?

Solution:

All factors of 150: 1, 2, 3, 5, 6,10, 15, 25, 30, 50, 75, and 150

The divisibility rule of 5 states that the numbers which end with the digits 0 and 5 are divisible by 5.

Hence, factors of 150 and multiples of 5 are 5, 10, 15, 25, 30, 50, 75, and 150.

3. What are the Common Factors of 150 and 141?

Solution:

All factors of 150: 1, 2, 3, 5, 6,10, 15, 25, 30, 50, 75, and 150

All factors of 141: 1 and 141

Therefore, the common factor of 150 and 141 is 1.