121 LearnersLast updated on May 26th, 2025
Factors of -32
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 -32, how they are used in real life, and tips to learn them quickly.
What are the Factors of -32?
The numbers that divide -32 evenly are known as factors of -32.
A factor of -32 is a number that divides the number without remainder.
The positive factors of 32 are 1, 2, 4, 8, 16, and 32.
Therefore, the factors of -32 include both positive and negative factors: 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, and -32.
Prime factors of 32: 2.
Prime factorization of 32: 2⁵.
The sum of positive factors of 32: 1 + 2 + 4 + 8 + 16 + 32 = 63.
How to Find Factors of -32?
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 -32. Identifying the numbers which are multiplied to get the number -32 is the multiplication method.
Step 1: Multiply -32 by -1, -32 × -1 = 32.
Step 2: Check for other numbers that give -32 after multiplying 1 × -32 = -32 2 × -16 = -32 4 × -8 = -32
Therefore, the factor pairs of -32 are: (-1, 32), (-2, 16), (-4, 8), and their negative counterparts.
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 -32 by -1, -32 ÷ -1 = 32.
Step 2: Continue dividing -32 by the numbers until the remainder becomes 0.
-32 ÷ -1 = 32
-32 ÷ 1 = -32
-32 ÷ -2 = 16
-32 ÷ 2 = -16
-32 ÷ -4 = 8
-32 ÷ 4 = -8
Therefore, the factors of -32 are: 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 32 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
The prime factor of 32 is 2.
The prime factorization of 32 is: 2⁵.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 32 is divided by 2 to get 16.
Step 2: Now divide 16 by 2 to get 8.
Step 3: Then divide 8 by 2 to get 4.
Step 4: Divide 4 by 2 to get 2. Here, 2 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 32 is: 2⁵.
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 32: (1, 32), (2, 16), and (4, 8).
Negative factor pairs of -32: (-1, -32), (-2, -16), and (-4, -8).
Common Mistakes and How to Avoid Them in Factors of -32
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 -32, 1 and -32 are also factors.
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 -32 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add a fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -32/1.5 = -21.333, 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 32 are prime numbers.
For example, 2 is the prime factor of 32, but it has other factors like 4, 8.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 32 as 2⁵ and missing all the key factors.
Factors of -32 Examples
Problem 1
There are 4 boxes and -32 apples. How will they distribute the apples equally?
Each box will have -8 apples.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of boxes.
-32/4 = -8
Problem 2
A construction project requires -32 beams, and each truck can carry 8 beams. How many trucks are needed?
4 trucks are needed.
Explanation
To find the number of trucks required, divide the total beams by the capacity of each truck.
-32/8 = -4 (Considering the absolute value, 4 trucks are needed).
Problem 3
A recipe requires -32 grams of sugar and is divided into 4 equal portions. How many grams are in each portion?
Each portion will have -8 grams of sugar.
Explanation
To find the sugar in each portion, divide the total grams by the number of portions.
-32/4 = -8
Problem 4
In a project, -32 tasks are to be completed by 8 teams. How many tasks will each team handle?
Each team will handle -4 tasks.
Explanation
Dividing the tasks by the total teams, we will get the number of tasks each team will handle.
-32/8 = -4
Problem 5
There are -32 chairs to be arranged in 4 rows. How many chairs will go in each row?
Each row will have -8 chairs.
Explanation
Divide the total chairs by the number of rows.
-32/4 = -8
FAQs on Factors of -32
1.What are the factors of -32?
2.Mention the prime factors of 32.
3.Is 32, a multiple of 4?
4.Mention the factor pairs of -32?
5.What is the square of -32?
Important Glossaries for Factors of -32
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -32 are 1, 2, 4, 8, 16, and 32, including their negative counterparts.
- Prime factors: The factors which are prime numbers. For example, 2 is the prime factor of 32.
- 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 -32 are (-1, -32), (-2, -16), etc.
- Negative factors: Factors of a number that are negative. For example, -1, -2, -4, -8, -16, and -32 are negative factors of -32.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 32 is 2⁵.
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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.
