125 LearnersLast updated on May 26th, 2025
Factors of -99
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 -99, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -99?
The numbers that divide -99 evenly are known as factors of -99.
A factor of -99 is a number that divides the number without remainder.
The positive factors of -99 are 1, 3, 9, 11, 33, and 99.
Negative factors of -99: -1, -3, -9, -11, -33, and -99.
Prime factors of -99: 3 and 11.
Prime factorization of 99: 3² × 11.
The sum of the absolute values of factors of -99: 1 + 3 + 9 + 11 + 33 + 99 = 156
How to Find Factors of -99?
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 -99. Identifying the numbers which are multiplied to get the number -99 is the multiplication method.
Step 1: Multiply -99 by 1, -99 × 1 = -99.
Step 2: Check for other numbers that give -99 after multiplying:
3 × -33 = -99
9 × -11 = -99
Therefore, the positive factor pairs of -99 are: (1, -99), (3, -33), and (9, -11).
All these factor pairs result in -99.
For every positive factor, there is a corresponding negative factor.
Finding Factors Using Division Method
Dividing the given number 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 -99 by 1, -99 ÷ 1 = -99.
Step 2: Continue dividing -99 by the numbers until the remainder becomes 0.
-99 ÷ 1 = -99
-99 ÷ 3 = -33
-99 ÷ 9 = -11
-99 ÷ 11 = -9
-99 ÷ 33 = -3
Therefore, the factors of -99 are: 1, 3, 9, 11, 33, 99, 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 -99 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
The prime factors of 99 are 3 and 11.
The prime factorization of 99 is 3² × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: First, divide 99 by 3 to get 33.
Step 2: Now divide 33 by 3 to get 11. Here, 11 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 99 is 3² × 11.
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 -99: (1, -99), (3, -33), and (9, -11).
Negative factor pairs of -99: (-1, 99), (-3, 33), and (-9, 11).
Common Mistakes and How to Avoid Them in Factors of -99
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 -99, 1 and -99 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 -99 consist of -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor is incorrect because -99/1.5 does not result in 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 -99 are prime numbers is incorrect.
For example, 3 and 11 are the prime factors of -99, but it has other factors like 9 and 33.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 99 as 3² × 11 and missing all the key factors.
Factors of -99 Examples
Problem 1
There are 11 teams and -99 points to distribute equally. How many points will each team receive?
Each team will get -9 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
-99/11 = -9
Problem 2
A garden plot is rectangular, the length of the plot is 9 meters, and the total area is -99 square meters. Find the width?
-11 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
-99 = 9 × width
To find the value of width, divide -99 by 9.
-99/9 = -11
Problem 3
There are 3 containers and -99 liters of liquid. How many liters will be in each container?
Each container will have -33 liters.
Explanation
To find the liters in each container, divide the total liters by the number of containers.
-99/3 = -33
Problem 4
In a class, there are 33 students, and -99 assignments to complete. How many assignments should each student do?
Each student should do -3 assignments.
Explanation
Dividing the assignments by the total number of students, we get the number of assignments each student should do.
-99/33 = -3
Problem 5
-99 tasks need to be divided among 9 workers. How many tasks will each worker handle?
Each worker will handle -11 tasks.
Explanation
Divide the total tasks by the number of workers.
-99/9 = -11
FAQs on Factors of -99
1.What are the factors of -99?
2.Mention the prime factors of -99.
3.Is -99 a multiple of 11?
4.Mention the factor pairs of -99?
5.What is the absolute value of the product of the factors of -99?
Important Glossaries for Factors of -99
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -99 are 1, 3, 9, 11, 33, 99, and their negative counterparts.
- Prime factors: The factors which are prime numbers. For example, 3 and 11 are prime factors of -99.
- 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 -99 are (1, -99), (3, -33), etc.
- Negative factors: These are the negative counterparts of the positive factors of a number. For example, -1, -3, -9, -11, -33, and -99 for -99.
- Prime factorization: Breaking down a number into the product of its prime factors. For example, the prime factorization of -99 is 3² × 11.
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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.
