126 LearnersLast updated on May 26th, 2025
Factors of -180
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of -180, how they are used in real life, and tips to learn them quickly.
What are the Factors of -180?
The numbers that divide -180 evenly are known as factors of -180.
A factor of -180 is a number that divides the number without a remainder.
The positive factors of -180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Negative factors of -180: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, and -180.
Prime factors of 180: 2, 3, and 5.
Prime factorization of 180: 2² × 3² × 5.
The sum of the positive factors of 180: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180 = 546
How to Find Factors of -180?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 180. Identifying the numbers which are multiplied to get the number 180 is the multiplication method.
Step 1: Multiply 180 by 1, 180 × 1 = 180.
Step 2: Check for other numbers that give 180 after multiplying
2 × 90 = 180
3 × 60 = 180
4 × 45 = 180
5 × 36 = 180
6 × 30 = 180
9 × 20 = 180
10 × 18 = 180
12 × 15 = 180
Therefore, the positive factor pairs of 180 are: (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18), (12, 15).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide 180 by 1, 180 ÷ 1 = 180.
Step 2: Continue dividing 180 by the numbers until the remainder becomes 0.
180 ÷ 1 = 180
180 ÷ 2 = 90
180 ÷ 3 = 60
180 ÷ 4 = 45
180 ÷ 5 = 36
180 ÷ 6 = 30
180 ÷ 9 = 20
180 ÷ 10 = 18
180 ÷ 12 = 15
Therefore, the factors of 180 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 180 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 180 are 2, 3, and 5.
The prime factorization of 180 is: 2² × 3² × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 180 is divided by 2 to get 90.
Step 2: Now divide 90 by 2 to get 45.
Step 3: Then divide 45 by 3 to get 15.
Step 4: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 180 is: 2² × 3² × 5.
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 180: (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18), (12, 15).
Negative factor pairs of -180: (-1, -180), (-2, -90), (-3, -60), (-4, -45), (-5, -36), (-6, -30), (-9, -20), (-10, -18), (-12, -15).
Common Mistakes and How to Avoid Them in Factors of -180
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 is 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 word. Always remember to include 1 and the number itself.
For example, in factors of -180, 1 and 180 is also a factor.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, The factors of -180 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 180/1.5 = 120, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of -180 are prime numbers. For example, 2, 3, and 5 are the prime factors of -180, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 180 as 2² × 3² × 5 and missing all the key factors.
Factors of -180 Examples
Problem 1
There are 36 apples and -180 oranges. How will they divide the oranges equally?
Each will get 5 oranges.
Explanation
To divide the oranges equally, we need to divide the total oranges with the number of apples.
-180/36 = 5
Problem 2
A garden is rectangular, the length of the garden is 15 meters and the total area is -180 square meters. Find the width?
-12 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
-180 = 15 × width
To find the value of width, we need to shift 15 to the left side.
-180/15 = width
Width = -12.
Problem 3
There are 45 boxes and -180 candies. How many candies will be in each box?
Each box will have 4 candies.
Explanation
To find the candies in each box, divide the total candies with the boxes.
-180/45 = 4
Problem 4
In a class, there are -180 students, and 9 groups. How many students are there in each group?
There are -20 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
-180/9 = -20
Problem 5
-180 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has -12 books.
Explanation
Divide total books with shelves.
-180/15 = -12
FAQs on Factors of -180
1.What are the factors of -180?
2.Mention the prime factors of -180.
3.Is -180 a multiple of 9?
4.Mention the factor pairs of -180?
5.What is the square of 180?
6.How can children in Bahrain use numbers in everyday life to understand Factors of -180?
7.What are some fun ways kids in Bahrain can practice Factors of -180 with numbers?
8.What role do numbers and Factors of -180 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of -180 skills?
Important Glossaries for Factor of -180
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180 along with their negative counterparts.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 180.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the positive factor pairs of 180 are (1, 180), (2, 90), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 180 is 2² × 3² × 5.
- Negative factors: Factors that are negative counterparts of positive factors. For example, the negative factors of -180 include -1, -2, -3, etc.
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About BrightChamps in Bahrain
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.
