129 LearnersLast updated on May 26th, 2025
Factors of -150
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of -150, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -150?
The numbers that divide -150 evenly are known as factors of -150.
A factor of -150 is a number that divides the number without remainder.
The positive factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
Therefore, the factors of -150 include their negative counterparts: -1, -2, -3, -5, -6, -10, -15, -25, -30, -50, -75, and -150.
Prime factors of 150: 2, 3, and 5.
Prime factorization of 150: 2 × 3 × 5².
The sum of positive factors of 150: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 150 = 372
How to Find Factors of -150?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give -150. Identifying the numbers which are multiplied to get the number -150 is the multiplication method.
Step 1: Multiply 150 by 1, 150 × 1 = 150.
Step 2: Check for other numbers that give 150 after multiplying
2 × 75 = 150
3 × 50 = 150
5 × 30 = 150
6 × 25 = 150
10 × 15 = 150
Therefore, the positive factor pairs of 150 are: (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), (10, 15).
All these factor pairs result in 150. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with the whole numbers until the remainder becomes zero and listing out the numbers that result as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 150 by 1, 150 ÷ 1 = 150.
Step 2: Continue dividing 150 by the numbers until the remainder becomes 0.
150 ÷ 1 = 150
150 ÷ 2 = 75
150 ÷ 3 = 50
150 ÷ 5 = 30
150 ÷ 6 = 25
150 ÷ 10 = 15
Therefore, the positive factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 150 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 150 are 2, 3, and 5.
The prime factorization of 150 is: 2 × 3 × 5².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 150 is divided by 2 to get 75.
Step 2: Now divide 75 by 3 to get 25.
Step 3: Then divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 150 is: 2 × 3 × 5².
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 150: (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15).
Negative factor pairs of -150: (-1, -150), (-2, -75), (-3, -50), (-5, -30), (-6, -25), and (-10, -15).
Common Mistakes and How to Avoid Them in Factors of -150
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the Number Itself and 1 as a Factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -150, 1 and 150 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -150 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because -150/1.5 = -100, but it is not a whole number.
Mistake 4
Confusing Factors with Prime Numbers
Remember that factors can be any whole numbers, not only primes. For example, thinking all the factors of -150 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 150, but it has other factors like 6 and 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 150 as 2 × 3 × 5² and missing all the key factors.
Factors of -150 Examples
Problem 1
There are 15 students and -150 apples. How will they divide it equally?
They will get -10 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of students.
-150/15 = -10
Problem 2
A rectangular plot has a width of 15 meters and a total area of -150 square meters. What is the length?
-10 meters.
Explanation
To find the length of the plot, we use the formula
Area = length × width
-150 = length × 15
To find the value of length, we need to shift 15 to the left side.
-150/15 = length Length = -10.
Problem 3
There are 30 crates and -150 oranges. How many oranges will be in each crate?
Each crate will have -5 oranges.
Explanation
To find the oranges in each crate, divide the total oranges by the number of crates.
-150/30 = -5
Problem 4
In a warehouse, there are -150 boxes and 5 sections. How many boxes are there in each section?
There are -30 boxes in each section.
Explanation
Dividing the boxes by the total sections, we get the number of boxes in each section.
-150/5 = -30
Problem 5
-150 books need to be arranged in 25 shelves. How many books will go on each shelf?
Each of the shelves has -6 books.
Explanation
Divide total books by shelves.
-150/25 = -6
FAQs on Factors of -150
1.What are the factors of -150?
2.Mention the prime factors of -150.
3.Is -150 a multiple of 5?
4.Mention the factor pairs of -150?
5.What is the absolute value of -150?
Important Glossaries for Factors of -150
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -150 include 1, 2, 3, 5, etc., and their negative counterparts.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 150.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 150 are (1, 150), (2, 75), etc.
- Prime factorization: Breaking down a number into its prime components. For example, the prime factorization of 150 is 2 × 3 × 5².
- Negative factors: The negative counterparts of the positive factors. For example, the negative factors of -150 include -1, -2, -3, etc.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
