103 LearnersLast updated on May 26th, 2025
Factors of -360
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 -360, how they are used in real life, and tips to learn them quickly.
What are the Factors of -360?
The numbers that divide -360 evenly are known as factors of -360.
A factor of -360 is a number that divides the number without a remainder.
The positive factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
Negative factors of -360: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -30, -36, -40, -45, -60, -72, -90, -120, -180, and -360.
Prime factors of 360: 2, 3, and 5.
Prime factorization of 360: 2³ × 3² × 5.
The sum of positive factors of 360: 1170.
How to Find Factors of -360?
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 pairs of numbers that are multiplied to give 360. Identifying the numbers that are multiplied to get the number 360 is the multiplication method.
Step 1: Multiply 360 by 1, 360 × 1 = 360.
Step 2: Check for other numbers that give 360 after multiplying
2 × 180 = 360
3 × 120 = 360
4 × 90 = 360
5 × 72 = 360
6 × 60 = 360
8 × 45 = 360
9 × 40 = 360
10 × 36 = 360
12 × 30 = 360
15 × 24 = 360
18 × 20 = 360
Therefore, the positive factor pairs of 360 are: (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), and (18, 20).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 360 by 1, 360 ÷ 1 = 360.
Step 2: Continue dividing 360 by the numbers until the remainder becomes 0.
360 ÷ 1 = 360
360 ÷ 2 = 180
360 ÷ 3 = 120
360 ÷ 4 = 90
360 ÷ 5 = 72
360 ÷ 6 = 60
360 ÷ 8 = 45
360 ÷ 9 = 40
360 ÷ 10 = 36
360 ÷ 12 = 30
360 ÷ 15 = 24
360 ÷ 18 = 20
Therefore, the factors of 360 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
Prime Factors and Prime Factorization
The factors can be found by dividing it by prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 360 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 360 are 2, 3, and 5.
The prime factorization of 360 is: 2³ × 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, 360 is divided by 2 to get 180.
Step 2: Now divide 180 by 2 to get 90.
Step 3: Then divide 90 by 2 to get 45.
Step 4: Divide 45 by 3 to get 15.
Step 5: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 360 is: 2³ × 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 360: (1, 360), (2, 180), (3, 120), (4, 90), (5, 72), (6, 60), (8, 45), (9, 40), (10, 36), (12, 30), (15, 24), and (18, 20).
Negative factor pairs of 360: (-1, -360), (-2, -180), (-3, -120), (-4, -90), (-5, -72), (-6, -60), (-8, -45), (-9, -40), (-10, -36), (-12, -30), (-15, -24), and (-18, -20).
Common Mistakes and How to Avoid Them in Factors of -360
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 number. Always remember to include 1 and the number itself.
For example, in factors of -360, 1 and 360 are also factors.
Factors of -360 Examples
Problem 1
There are 10 teams and 360 players. How will they distribute the players equally among the teams?
Each team will have 36 players.
Explanation
To distribute the players equally, we need to divide the total players by the number of teams.
360/10 = 36.
Problem 2
A rectangular hall has a width of 12 meters and a total area of 360 square meters. Find the length.
30 meters.
Explanation
To find the length of the hall, we use the formula, Area = length × width 360 = length × 12
To find the value of length, we need to shift 12 to the left side.
360/12 = length
Length = 30.
Problem 3
There are 18 boxes and 360 items. How many items will be in each box?
Each box will have 20 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
360/18 = 20.
Problem 4
In a school, there are 36 teachers, and 360 students. How many students are assigned to each teacher?
There are 10 students assigned to each teacher.
Explanation
Dividing the students by the total number of teachers, we will get the number of students per teacher.
360/36 = 10.
Problem 5
360 pages need to be printed, and there are 15 printers. How many pages will each printer print?
Each printer will print 24 pages.
Explanation
Divide total pages by the number of printers.
360/15 = 24.
FAQs on Factors of -360
1.What are the factors of 360?
2.Mention the prime factors of 360.
3.Is 360 a multiple of 9?
4.Mention the factor pairs of 360?
5.What is the square of 360?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of -360?
7.What are some fun ways kids in United Kingdom can practice Factors of -360 with numbers?
8.What role do numbers and Factors of -360 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of -360 skills?
Important Glossaries for Factors of -360
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 360.
- 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 360 are (1, 360), (2, 180), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For 360, this is 2³ × 3² × 5.
- Negative factors: Negative numbers that divide the original number without leaving a remainder. For example, the negative factors of -360 include -1, -2, -3, -4, 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.
