103 LearnersLast updated on June 4th, 2025
Factors of -40
Factors are the numbers that divide any given number evenly without 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 -40, how they are used in real life, and tips to learn them quickly.
What are the Factors of -40?
The numbers that divide -40 evenly are known as factors of -40.
A factor of -40 is a number that divides the number without remainder.
The positive factors of -40 are 1, 2, 4, 5, 8, 10, 20, and 40.
Negative factors of -40: -1, -2, -4, -5, -8, -10, -20, and -40.
Prime factors of 40 (ignoring the sign): 2 and 5.
Prime factorization of 40: 23 × 5.
The sum of the positive factors of 40: 1 + 2 + 4 + 5 + 8 + 10 + 20 + 40 = 90
How to Find Factors of -40?
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 -40. Identifying the numbers which are multiplied to get the number -40 is the multiplication method.
Step 1: Multiply -40 by 1, -40 × 1 = -40.
Step 2: Check for other numbers that give -40 after multiplying -2 × 20 = -40
-4 × 10 = -40
-5 × 8 = -40
Therefore, the positive factor pairs of -40 are: (1, -40), (2, -20), (4, -10), (5, -8).
For every positive factor, there is a 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 -40 by 1,
-40 ÷ 1 = -40.
Step 2: Continue dividing -40 by the numbers until the remainder becomes 0.
-40 ÷ 1 = -40
-40 ÷ 2 = -20
-40 ÷ 4 = -10
-40 ÷ 5 = -8
Therefore, the factors of -40 are: 1, 2, 4, 5, 8, 10, 20, 40.
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 40 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1
The prime factors of 40 are 2 and 5.
The prime factorization of 40 is: 23 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 40 is divided by 2 to get 20.
Step 2: Now divide 20 by 2 to get 10.
Step 3: Then divide 10 by 2 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 40 is: 23 × 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 -40: (1, -40), (2, -20), (4, -10), (5, -8).
Negative factor pairs of -40: (-1, 40), (-2, 20), (-4, 10), (-5, 8).
Common Mistakes and How to Avoid Them in Factors of -40
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 -40, 1 and -40 are also factors.
Factors of -40 Examples
Problem 1
There are 4 teams and 40 points to distribute equally among them. How will they divide it equally?
They will get 10 points each.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
40/4 = 10
Problem 2
A fence is 10 meters long, and the total area to be fenced is 40 square meters. Find the width of the fenced area?
4 meters.
Explanation
To find the width of the fenced area, we use the formula, Area = length × width
40 = 10 × width
To find the value of width, we need to shift 10 to the left side.
40/10 = width
Width = 4.
Problem 3
There are 5 boxes and 40 apples. How many apples will be in each box?
Each box will have 8 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
40/5 = 8
Problem 4
In a class, there are 40 students, and they are divided into 8 groups. How many students are there in each group?
There are 5 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
40/8 = 5
Problem 5
40 books need to be placed on 10 shelves. How many books will go on each shelf?
Each of the shelves has 4 books.
Explanation
Divide the total books by the number of shelves.
40/10 = 4
FAQs on Factors of -40
1.What are the factors of -40?
2.Mention the prime factors of 40.
3.Is -40 a multiple of 5?
4.Mention the factor pairs of -40?
5.What is the square of 40?
Important Glossaries for Factors of -40
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -40 are 1, 2, 4, 5, 8, 10, 20, and 40.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 40.
- 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 -40 are (1, -40), (2, -20), etc.
- Negative factors: Factors that are negative numbers. For instance, -1, -2, -4, -5, are negative factors of -40.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 40 is 23 × 5.
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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.
