103 LearnersLast updated on May 26th, 2025
Factors of -400
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 -400, how they are used in real life, and tips to learn them quickly.
What are the Factors of -400?
The numbers that divide -400 evenly are known as factors of -400.
A factor of -400 is a number that divides the number without remainder.
The positive factors of -400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.
Negative factors of -400: -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -200, and -400.
Prime factors of -400: 2 and 5.
Prime factorization of 400: 24 × 52.
The sum of positive factors of 400: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 200 + 400 = 861.
How to Find Factors of -400?
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 -400. Identifying the numbers which are multiplied to get the number -400 is the multiplication method.
Step 1: Multiply -400 by 1, -400 × 1 = -400.
Step 2: Check for other numbers that give -400 after multiplying
2 × -200 = -400
4 × -100 = -400
5 × -80 = -400
8 × -50 = -400
10 × -40 = -400
16 × -25 = -400
20 × -20 = -400
25 × -16 = -400
Therefore, the positive factor pairs of 400 are: (1, 400), (2, 200), (4, 100), (5, 80), (8, 50), (10, 40), (16, 25), (20, 20). All these factor pairs result in 400. 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 a simple division method -
Step 1: Divide -400 by 1, -400 ÷ 1 = -400.
Step 2: Continue dividing -400 by the numbers until the remainder becomes 0.
-400 ÷ 1 = -400
-400 ÷ 2 = -200
-400 ÷ 4 = -100
-400 ÷ 5 = -80
-400 ÷ 8 = -50
-400 ÷ 10 = -40
-400 ÷ 16 = -25
Therefore, the factors of -400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400, and their negative counterparts.
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 400 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
400 ÷ 2 = 200
200 ÷ 2 = 100
100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 400 are 2 and 5.
The prime factorization of 400 is: 24 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 400 is divided by 2 to get 200.
Step 2: Now divide 200 by 2 to get 100.
Step 3: Then divide 100 by 2 to get 50.
Step 4: Divide 50 by 2 to get 25.
Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 400 is: 24 × 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 400: (1, 400), (2, 200), (4, 100), (5, 80), (8, 50), (10, 40), (16, 25).
Negative factor pairs of -400: (-1, -400), (-2, -200), (-4, -100), (-5, -80), (-8, -50), (-10, -40), (-16, -25).
Common Mistakes and How to Avoid Them in Factors of -400
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 -400, 1 and 400 are also factors.
Factors of -400 Examples
Problem 1
A construction company has 400 bricks. If they distribute them equally in 8 stacks, how many bricks will each stack have?
Each stack will have 50 bricks.
Explanation
To distribute the bricks equally, we need to divide the total bricks by the number of stacks.
400/8 = 50
Problem 2
A rectangular garden has a length of 10 meters and a total area of 400 square meters. Find the width.
40 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
400 = 10 × width
To find the value of width, we need to shift 10 to the left side.
400/10 = width Width = 40.
Problem 3
There are 20 boxes and 400 chocolates. How many chocolates will be in each box?
Each box will have 20 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates by the boxes.
400/20 = 20
Problem 4
In a class, there are 400 students, and 5 groups. How many students are there in each group?
There are 80 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
400/5 = 80
Problem 5
A bookstore has 400 books and 10 shelves. How many books will go on each shelf?
Each shelf will have 40 books.
Explanation
Divide total books by shelves.
400/10 = 40
FAQs on Factors of -400
1.What are the factors of -400?
2.Mention the prime factors of -400.
3.Is -400 a multiple of 4?
4.Mention the factor pairs of -400.
5.What is the square of 400?
6.How can children in Thailand use numbers in everyday life to understand Factors of -400?
7.What are some fun ways kids in Thailand can practice Factors of -400 with numbers?
8.What role do numbers and Factors of -400 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of -400 skills?
Important Glossaries for Factors of -400
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400, and their negatives.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of -400.
- 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 -400 are (1, 400), (2, 200), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 400 is 24 × 52.
- Multiples: Numbers that can be divided by a specific number without a remainder. For example, -400 is a multiple of 4.
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About BrightChamps in Thailand
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.
