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Factors

Factors of 150 | Prime Factorization of 150 | Factor Tree of 150

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 150 | Prime Factorization of 150 | Factor Tree of 150

Factors of 150 | Prime Factorization of 150 | Factor Tree of 150

Factors of 150 are the numerals that divide the original number into equal parts. They are also whole numbers. Furthermore, factors of 150 will divide these numbers evenly. These factors can either be negative or positive. However, these factors can’t be decimals or fraction numbers.

When it comes to factors of 150, it has a total of 12 factors. They are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

What Are the Factors of 150?

The factors of 150 are the numbers that divide the number (150) evenly without leaving any remainder. As 150 is a composite number, it means it has more than two factors, including 1 and the number itself. As it is a composite, these factors are also negative or positive. Here are the number 150 has both positive and negative factors.

Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150
Negative Factors of 150-1, -2, -3, -5, -6, -10, -15, -25, -30, -75, and -150
Prime Factorization of 150: 2 X 3 X 5 X 5 or 2 X 3 X 52
Prime Factors of 150: 2, 3, and 5
Sum of Factors of 150372
Sum of Prime Factors of 150: 10

What Are the Factors of 150 in Pairs?

A pair factor of 150 is a combination of two numbers, which when multiplied together gives the product of the original number (150). These pair factors are also written in positive and negative pairs as shown in the table below:

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).

1 X 150 = 1502 X 75 = 150
3 X 50 = 1505 X 30 = 150
6 X 25 = 15010 X 15 = 150
15 X 10 = 15025 X 6 = 150
30 X 5 = 15050 X 3 = 150
75 X 2 = 150150 X 1 = 150

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).

-1 X -150 = 150-2 X -75 = 150
-3 X -50 = 150-5 X -30 = 150
-6 X -25 = 150-10 X -15 = 150
-15 X -10 = 150-25 X -6 = 150
-30 X -5 = 150-50 X -3 = 150
-75 X -2 = 150-150 X -1 = 150

How To Find Factors of 150 Through Division Method?

Through this method, we will understand how to find factors of 150 through division in a simple way. Since 150 is a number that can be divided by 2, it means it is a factor of 150. That is how we perform the division method. Now, we will take every integer and divide it by 150, and the ones that leave no remainder are the factors of 150. Let’s see this method.

  • 150 ÷ 1 = 150
  • 150 ÷ 2 = 75
  • 150 ÷ 3 = 25
  • 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

Hence, we can see that 1, 2, 3, 5, 6, 10, 15, 35, 30, 50, 70, and 150 are the factors of 150.

What Is the Prime Factorisation of 150?

Check if the given number is a prime number. If the given number is a prime number, then it has only two factors: 1 and 150. If the given number is a composite number, then it has more than two factors.

Since 150 is the composite number, we have more than two factors. Hence, we can use the prime factorization method to find the factors of 150.

The steps to find prime factors of 150 using the prime factorization method are given below:

  • Step 1: Firstly, we will take the smallest prime factor to divide by 150, that is 2.
    • 150 ÷ 2 = 75
  • Step 2: Now, we will take another small prime number to divide 75 with as we cannot divide it with 2. So, we will take 3.
    • 75 ÷ 3 = 25
  • Step 3: As 25 can
    • 25 ÷ 5 = 5
    • 5 ÷ 5 = 1

The quotient is 1. Since 1 cannot be divided further, the prime factors of 150 are 2 X 3 X 5 X 5 or 2 X 3 X 52. We can also write it down as 2, 3, and 5, as both of them are prime numbers.

Image representation of the prime factorization of 150:

Prime Factorization of 150

What is the Factor Tree of 150?

Students can also use the factor tree to find the prime factors of 150. In this method, we will place the number 150 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of the given number (150). Now, again, we will split the pair of factors into factors. This process will be continued until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 150.

  • Step 1: Let’s place the number 150 at the top of the factor tree and write down 150 in pairs, that is, 10 and 15.
  • Step 2: Since 10 is not a prime number, we will now divide 10 into 2 and 5.
  • Step 3: Since 2 and 5 are prime numbers, we can no longer separate them.
  • Step 4: As we can see, 15 is not a prime number, so we will split 15 into 3 and 5.
  • Step 5: We can see that 3 and 5 are both prime numbers. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 2 X 3 X 52 or 2 X 3 X 5 X 5= 150, which are 150 prime factors.

There are many ways in which we can write the factor tree of 150. Below is an image representation of the factor tree of 150

Factor Tree of 150

Solved Examples on Factors of 150

Below are some solved examples on factors of 150 for students.

What is the sum of all the factors of 150?
1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150 are the 150 factors.
1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 75 + 150 = 372
Hence, 372 is the sum of all 150 factors.

What’s the highest common factor between 150 and 120?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150.
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Hence, from the above, the common factors of 150 and 120 are 1, 2, 3, 5, 6, 10, 15, and 30.
The highest common factor between 150 and 120 is 30.

What’s the highest common factor between 150 and 250?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150.
Factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.
Hence, from the above, the common factors of 150 and 250 are 1, 2, 5, 10, and 25.
The highest common factor between 150 and 250 is 25.

Is 75 a factor of 150?
Yes, 75 is a factor of 150.
As 150 ÷ 75 = 2.

What is the largest factor of 150?
The largest factor of 150 is 150.
The second largest factor of 150 is 75.

What are the first 5 factors of 150?
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150.
The first 5 factors of 150 are 1, 2, 3, 5, and 6.

Is 125 a factor of 150?
No, 125 is not a factor of 150.
As 150 ÷ 125 = Leaves a reminder
Hence, 125 is not a factor of 150 since factors of a number (150) don’t leave a remainder after being divided.

FAQs on Factors of 150

What are the factors and prime factors of 150?
The 150 factors are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150.
The 150 prime factors are: 2 X 3 X 52 or 2 X 3 X 5 X 5.

How many 150 factors are odd?
A total of 6 odd numbers are there in factors of 150 and they are 1, 3, 5, 15, 25, and 75.

What are the factors of -150?
The factors of -150 are -1, -2, -3, -5, -6, -10, -15, -25, -30, -75, and -150.

How many pair factors are there in 150?
A total of 6 pairs are there in factors of 150.

What are the composite factors of 150?
6, 10, 15, 25, 30, 75, and 150 are the 150 composite factors. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 150 in pairs?
(1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15) are the 150 factors of pairs.

What are the positive factors for 150?
1, 2, 3, 4, 6, 8,1, 2, 3, 5, 6, 10, 15, 25, 30, 75, and 150 are the positive factors for 150.

Now that you have all the necessary information regarding the factors of 150, We hope this article has been useful for you and easy to understand as well.

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Prerit Jain

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