126 LearnersLast updated on May 26th, 2025
Factors of -192
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 -192, how they are used in real life, and tips to learn them quickly.
What are the Factors of -192?
The numbers that divide -192 evenly are known as factors of -192.
A factor of -192 is a number that divides the number without a remainder.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.
Negative factors of -192: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, and -192.
Prime factors of 192: 2 and 3.
Prime factorization of 192: 26 × 3.
The sum of factors of 192: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 192 = 511
How to Find Factors of -192?
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 192. Identifying the numbers which are multiplied to get the number 192 is the multiplication method.
Step 1: Multiply 192 by 1, 192 × 1 = 192.
Step 2: Check for other numbers that give 192 after multiplying 2 × 96 = 192 3 × 64 = 192 4 × 48 = 192 6 × 32 = 192 8 × 24 = 192 12 × 16 = 192
Therefore, the positive factor pairs of 192 are: (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), (12, 16).
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 in whole numbers as factors. Factors can be calculated using the simple division method:
Step 1: Divide 192 by 1, 192 ÷ 1 = 192.
Step 2: Continue dividing 192 by the numbers until the remainder becomes 0.
192 ÷ 1 = 192
192 ÷ 2 = 96
192 ÷ 3 = 64
192 ÷ 4 = 48
192 ÷ 6 = 32
192 ÷ 8 = 24
192 ÷ 12 = 16
Therefore, the factors of -192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
Prime Factors and Prime Factorization
The factors can be found by dividing them by 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 192 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
192 ÷ 2 = 96
96 ÷ 2 = 48
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
The prime factors of 192 are 2 and 3.
The prime factorization of 192 is: 2^6 × 3.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 192 is divided by 2 to get 96.
Step 2: Now divide 96 by 2 to get 48.
Step 3: Then divide 48 by 2 to get 24.
Step 4: Continue dividing by 2 until you reach the prime number 3. So, the prime factorization of 192 is: 26 × 3.
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 192: (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), (12, 16).
Negative factor pairs of -192: (-1, -192), (-2, -96), (-3, -64), (-4, -48), (-6, -32), (-8, -24), (-12, -16).
Common Mistakes and How to Avoid Them in Factors of -192
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 whole number. Always remember to include 1 and the number itself.
For example, in factors of -192, 1 and 192 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of -192 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 192/1.5 = 128, 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 -192 are prime numbers. For instance, 2 and 3 are the prime factors of 192, but it has other factors like 4, 6, etc.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing the wrong factors.
For example, not breaking 192 as 2^6 × 3 and missing all the key factors.
Factors of -192 Examples
Problem 1
A bookshelf has -192 books, and each shelf can hold 16 books. How many shelves are needed?
12 shelves are needed.
Explanation
To determine the number of shelves needed, divide the total books by the books per shelf.
192/16 = 12
Problem 2
A rectangular ice rink has a length of 32 meters, and the total area is -192 square meters. Find the width.
6 meters.
Explanation
To find the width of the ice rink, we use the formula,
Area = length × width
192 = 32 × width
To find the value of width, divide the area by the length.
192/32 = width Width = 6
Problem 3
There are 24 boxes and -192 candies. How many candies will be in each box?
Each box will have 8 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
192/24 = 8
Problem 4
In a school, there are -192 students, and 8 groups. How many students are there in each group?
There are 24 students in each group.
Explanation
Dividing the students by the total groups will give the number of students in each group.
192/8 = 24
Problem 5
-192 flyers need to be distributed in 12 locations. How many flyers will go to each location?
Each location will receive 16 flyers.
Explanation
Divide the total flyers by the number of locations.
192/12 = 16
FAQs on Factors of -192
1.What are the factors of -192?
2.Mention the prime factors of -192.
3.Is -192 a multiple of 3?
4.Mention the factor pairs of -192.
5.What is the square of -192?
Important Glossaries for Factors of -192
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 192.
- 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 -192 are (1, 192), (2, 96), etc.
- Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 192 is 2^6 × 3.
- Multiplication method: A method used to find factors by identifying pairs of numbers that multiply to give the original number.
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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.
