103 LearnersLast updated on May 26th, 2025
Factors of -60
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 -60, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -60?
The numbers that divide -60 evenly are known as factors of -60.
A factor of -60 is a number that divides the number without remainder.
The factors of -60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Negative factors of -60: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -30, and -60.
Prime factors of -60: 2, 3, and 5.
Prime factorization of -60: -1 × 22 × 3 × 5.
The sum of factors of 60: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 30 + 60 = 168
How to Find Factors of -60?
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 -60. Identifying the numbers which are multiplied to get the number -60 is the multiplication method.
Step 1: Multiply -60 by 1, -60 × 1 = -60.
Step 2: Check for other numbers that give -60 after multiplying
2 × -30 = -60
3 × -20 = -60
4 × -15 = -60
5 × -12 = -60
6 × -10 = -60
Therefore, the positive factor pairs of -60 are: (1, -60), (2, -30), (3, -20), (4, -15), (5, -12), and (6, -10).
For each positive factor, there is a corresponding negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 a simple division method
Step 1: Divide -60 by 1, -60 ÷ 1 = -60.
Step 2: Continue dividing -60 by the numbers until the remainder becomes 0.
-60 ÷ 1 = -60
-60 ÷ 2 = -30
-60 ÷ 3 = -20
-60 ÷ 4 = -15
-60 ÷ 5 = -12
-60 ÷ 6 = -10
Therefore, the factors of -60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
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 -60 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
-60 ÷ -1 = 60
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of -60 are 2, 3, and 5.
The prime factorization of -60 is: -1 × 22 × 3 × 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, -60 is divided by -1 to get 60.
Step 2: Now divide 60 by 2 to get 30.
Step 3: Then divide 30 by 2 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 -60 is: -1 × 22 × 3 × 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 -60: (1, -60), (2, -30), (3, -20), (4, -15), (5, -12), and (6, -10).
Negative factor pairs of -60: (-1, 60), (-2, 30), (-3, 20), (-4, 15), (-5, 12), and (-6, 10).
Common Mistakes and How to Avoid Them in Factors of -60
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -60, 1 and -60 are also factors.
Factors of -60 Examples
Problem 1
There are 6 teams and -60 points to distribute. How will they distribute it equally?
Each team will receive -10 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
-60/6 = -10
Problem 2
A rectangular garden has a length of 15 meters and a total area of -60 square meters. Find the width.
-4 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width -60 = 15 × width
To find the value of width, we need to shift 15 to the left side.
-60/15 = width
Width = -4.
Problem 3
There are 3 crates and -60 apples. How many apples will be in each crate?
Each crate will have -20 apples.
Explanation
To find the apples in each crate, divide the total apples by the crates.
-60/3 = -20
Problem 4
In a competition, there are -60 penalty points and 5 groups. How many penalty points are there in each group?
There are -12 penalty points in each group.
Explanation
Dividing the penalty points with the total groups, we will get the number of penalty points in each group.
-60/5 = -12
Problem 5
-60 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has -15 books.
Explanation
Divide total books with shelves.
-60/4 = -15
FAQs on Factors of -60
1.What are the factors of -60?
2.Mention the prime factors of -60.
3.Is -60 a multiple of 3?
4.Mention the factor pairs of -60?
5.What is the square of -60?
6.How can children in Qatar use numbers in everyday life to understand Factors of -60?
7.What are some fun ways kids in Qatar can practice Factors of -60 with numbers?
8.What role do numbers and Factors of -60 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of -60 skills?
Important Glossaries for Factor of -60
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
- Negative factors: Factors of a number that are negative. For example, -1, -2, -3, etc., are negative factors of -60.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of -60.
- 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 -60 are (1, -60), (2, -30), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For -60, it is -1 × 2^2 × 3 × 5.
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About BrightChamps in Qatar
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.
