Factors of 150—with easy division and prime factorization

ECTI Pakistan - Factors of 150

Factors of 150

In mathematics, factors of 150 are whole numbers that divide an original number into equal parts. 

The factors of 150 will divide it equally. Fractions or decimal numbers cannot be included in these factors. There are a total of 12 factors of 150. The numbers are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. All the factors of 150 add up to 372.

When two numbers are multiplied together, the pair factors of 150 result in 150. For example, the factor pairs for 47 are (1, 47) and (-1, 47). Multiplying a pair of negative factors gives the original number. For example, multiplying -1 * -47 gives the number 47. Therefore, 47 can have both positive and negative factors. The factor pairs of the number 150 are whole numbers that can be positive or negative, but not a fraction or decimal number.

What are the Factors of 150?

Factors of 150 are the numbers that divide 150 exactly and do not leave a remainder. The number 150 has more factors than just 1 and 150 because it is an even composite number. 

Therefore, 150 has the following factors: 

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

ECTI Pakistan - Factors of 150

What are Factors of -150?

When we multiply two numbers, and we get -150 as a product, those numbers are the factors of -150. 

Here is the explanation:

-1 × 150 = -150 

 1 × -150 = -150

 -2 × 75 = -150 

 2 × -75 = -150 

 -3 × 50 = -150 

 3 × -50 = -150 

 -5 × 30 = -150 

 5 × -30 = -150

 -6 × 25 = -150 

 6 × -25 = -150

 -10 × 15 = -150

  10 × 15 = -150

We can get -150 by having (-1, 150), (-2, 75), (-3, 50), (-5, 30), (-6, 25), and (-10, 15) as a pair of factors. Similarly, we can also get -150 by having(1, -150), (2, -75), (3, -50), (5, -30), (6, -25), and (10, -15) as a pair of factors.

How to Find Factors of 150?

In order to find the 150 factors, there are two methods:

  • Division method
  • Prime factorization of 150

Factors of 150 by Division Method

We will use this method to divide by a simple arithmetic function. We can see that 150 is an even number, so it can be divided by 2. Therefore, 2 is a factor of 150. Let’s see how many numbers 150 can be evenly divided into.

150/1 = 150

150/2 = 75

150/3 = 50

150/5 = 30

150/6 = 25

150/10 = 15

150/15 = 10

150/25 = 6

150/30 = 5

150/50 = 3

150/75 = 2

150/150 = 1

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

Prime Factorization of 150

As a composite number, 150 has prime factors. Let’s find out how to calculate the prime factors of 150.

ECTI Pakistan - Factors of 150

Step 1:

First, divide 150 by the smallest prime number, let’s say 2.

150 ÷ 2 = 75

Step 2:

If you divide 75 by 2, you will get a fraction. Divide that by the next prime number, say 3.

75 ÷ 3 = 25

Step 3:

Dividing 25 by 3 again gives you a fractional number, so carry on to the next prime number, say 55.

25 ÷ 5 = 5

5 ÷ 5 = 1

After the division process was completed, we received the number 1. As a result, we cannot proceed. Therefore, the prime factors of 150 are 2 × 3 × 5 × 5 or 2 × 3 × 52, where 2, 3, and 5 are prime numbers.

With the help of prime factorization, it is possible to find out the number of factors of the number 150. There are 3 prime factors and 52 factors in the number 150. For the prime factorization, the exponents are 1, 1, and 2. Multiply the exponents with the number 1. (1+1)(1+1)(2+1) =2 × 2 × 3= 12. Therefore, there are 12 factors in the number 150.

Pair Factors of 150

A pair factor is an integer that is multiplied together to get the original number. When multiplying two numbers in a pair to get 150, such numbers are as follows:

Positive Factors of 150Positive 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)

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

Negative Factors of 150Negative 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)

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

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Solved Examples

Example 1:

Calculate 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.

Since 151 is a prime number, the common factor between 150 and 151 is 1.

Example 2:

Calculate 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.

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

Example 3:

Find the common factor between 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.

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

Practice Questions

  1. Find out if 4 is a factor of 150. Explain why.
  2. What are the even factors of 150?
  3. What is the sum of 150’s prime factors?

FAQ’s

What are the factors of 150?

Factors of 150 = 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 = 2 × 3 × 5 × 5 or 2 × 3 × 52.

What are the positive pair factors of 150?

The positive pair factors of 150 = (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 = (-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. 25 is a factor of 150 because it divides 150 exactly without leaving a remainder.

What is the sum of all factors of 150?

The sum of all factors of 150 is 372.
1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 150 = 372