 # Factors of 150

The factors of 150 are the numbers that produce the result as 150 when two numbers are multiplied together. Consider an example, the factor pairs of 47 are written as (1, 47) and (-1,-47). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × -47 then we get the number 47. Thus, we can consider both positive and negative factor pairs of 47. Factor pairs of the number 150 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 150, we will use the factorization method.

In the factorization method, first take the numbers, 1 and 150 as factors of 150 and proceed with finding the other pairs of multiples of 150 which gives the results equal to the original number. To understand this method in a better way, read the article below; to find factor 150 in pairs and also the prime factorization of 150.

## What are the Factors of 150?

The factors of 150 are the numbers that divide 150 exactly without leaving any remainder. In other words, the factors of 150 are the numbers that are multiplied in pairs resulting in an original number. As the number 150 is an even composite number, 150 has many factors other than 1 and 150. Thus, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

 Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150 Prime Factorization of 150: 2×3×5×5 or 2 × 3 × 52

## Pair Factors of 150

To find the pair factors of 150, multiply the two numbers in a pair to get the original number as 150, such numbers are as follows:

If 1 × 150 = 150, then (1, 150) is a pair factor of 150.

Similarly,

2 × 75 = 150, (2, 75) is a pair factor of 150

3 × 50 = 150, (3, 50) is a pair factor of 150

5 × 30 = 150, (5, 30) is a pair factor of 150

6 × 25 = 150, (6, 25) is a pair factor of 150

10 × 15 = 150, (10, 15) is a pair factor of 150

 Positive Factors of 150 Positive Pair Factors of 150 1 × 150 (1, 150) 2 × 75 (2, 75) 3 × 50 (3, 50) 5 × 30 (5, 30) 6 × 25 (6, 25) 10 × 15 (10, 15)

Therefore, the positive factor pairs  of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).

To find the negative pair factors of 150, then proceed with the following steps

If -1 × -150 = 150, then (-1, -150) is a pair factor of 150.

Similarly,

-2 × -75 = 150, (-2, -75) is a pair factor of 150

-3 × -50 = 150, (-3, -50) is a pair factor of 150

-5 × -30 = 150, (-5, -30) is a pair factor of 150

-6 × -25 = 150, (-6, -25) is a pair factor of 150

-10 × -15 = 150, (-10, -15) is a pair factor of 150

 Negative Factors of 150 Negative Pair Factors of 150 -1 × -150 (-1, -150) -2 × -75 (-2, -75) -3 × -50 (-3, -50) -5 × -30 (-5, -30) -6 × -25 (-6, -25) -10 × -15 (-10, -15)

Therefore, the negative factor pairs of 150 are (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).

## How to Calculate the Prime Factors of 150?

Observe the following steps to calculate the factors of 150.

• First, write the number 150
• Find the two numbers, which gives the result as 150 under the multiplication, say 2 and 75, such as 2 × 75 = 150.
• We know that 2 is a prime number that has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized.

2 = 2 × 1

• But look at the number 75, which is a composite number and it can be further factorized.

75 can be factored as 5 x 5 x 3 x 1

• Therefore, the factorization of 150 is written as: 150 = 1 x 2 x 3 x 5 x 5
• Finally, write down all the unique numbers that are obtained as factors, such as 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150

## Prime Factorization of 150

The number 150 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 150.

Step 1: The first step is to divide the number 150 with the smallest prime number, say 2.

150 ÷ 2 = 75

Step 2: You will get a fractional number if you divide 75 by 2. Continue with the next prime number, say 3.

75 ÷ 3 = 25

Step 3: Again you will get a fractional value when you divide 25 by 3 hence, continue with the next prime number say 5.

25 ÷ 5 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 150 are written as 2 x 3 x 5 x 5 or 2 x 3 x 52, where 2, 3 and 5 are the prime numbers.

It is possible to find the exact number of factors of a number 150 with the help of prime factorization. The prime factor representation of 150 is 2 x 3 x 52. The exponents in the prime factorization are 1, 1 and 2. Add the number 1 with the exponents and multiply it. (1+1)(1+1)(2+1) =2 x 2 x 3= 12. Therefore, the number 150 has 12 factors.

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### Examples

Example 1:

Find the common factors of 150 and 151.

Solution:

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

The factors of 151 are 1 and 151.

As the number 151 is a prime number, the common factor of 150 and 151 is 1.

Example 2:

Find the common factors of 150 and 149.

Solution:

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

Factors of 149 = 1 and 149.

Therefore, the common factor of 150 and 149 is 1, as 149 is a prime number.

Example 3:

Find the common factors of 150 and 125.

Solution:

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

The factors of 125 are 1, 5, 25, 125.

Therefore, the common factors of 150 and 125 are 1, 5 and 25.

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## Frequently Asked Questions 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.

### What is the prime factorization of 150?

The prime factorization of 150 is 2 x 3 x 5 x 5 or 2 x 3 x 52.

### What are the positive pair factors of 150?

The positive pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).

### What are the negative pair factors of 150?

The negative pair factors of 150 are (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).

### Is 25 a factor of 150?

Yes, 25 is a factor of 150. As the number 25 divides 150 exactly without leaving a remainder, 25 is a factor of 150.

Quiz on Factors of 150

#### 1 Comment

1. Shrutimala Phukan

Thanks for Information