122 LearnersLast updated on May 26th, 2025
Factors of -117
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 -117, how they are used in real life, and tips to learn them quickly.
What are the Factors of -117?
The numbers that divide -117 evenly are known as factors of -117.
A factor of -117 is a number that divides the number without a remainder.
The positive factors of 117 are 1, 3, 9, 13, 39, and 117.
Negative factors of -117: -1, -3, -9, -13, -39, -117.
Prime factors of 117: 3 and 13.
Prime factorization of 117: 3² × 13.
The sum of factors of 117 (ignoring negatives for simplicity): 1 + 3 + 9 + 13 + 39 + 117 = 182
How to Find Factors of -117?
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 117. Identifying the numbers which are multiplied to get the number 117 is the multiplication method.
Step 1: Multiply 117 by 1, 117 × 1 = 117.
Step 2: Check for other numbers that give 117 after multiplying
3 × 39 = 117
9 × 13 = 117
Therefore, the positive factor pairs of 117 are: (1, 117), (3, 39), (9, 13).
All these factor pairs result in 117.
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 the simple division method
Step 1: Divide 117 by 1, 117 ÷ 1 = 117.
Step 2: Continue dividing 117 by the numbers until the remainder becomes 0.
117 ÷ 1 = 117
117 ÷ 3 = 39
117 ÷ 9 = 13
Therefore, the factors of -117 are: -1, -3, -9, -13, -39, -117, 1, 3, 9, 13, 39, 117.
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 117 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 117 are 3 and 13.
The prime factorization of 117 is: 3² × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 117 is divided by 3 to get 39.
Step 2: Now divide 39 by 3 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 117 is: 3² × 13.
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 117: (1, 117), (3, 39), (9, 13).
Negative factor pairs of -117: (-1, -117), (-3, -39), (-9, -13).
Common Mistakes and How to Avoid Them in Factors of -117
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 -117, 1 and -117 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 -117 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, because -117/1.5 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 -117 are prime numbers.
For example, 3 and 13 are the prime factors of 117, but it has other factors like 9 and 39.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 117 as 3² × 13 and missing all the key factors.
Factors of -117 Examples
Problem 1
A factory produces 117 gadgets and they need to be packaged in boxes with equal numbers. If each box holds 13 gadgets, how many boxes are needed?
9 boxes are needed.
Explanation
To find the number of boxes, divide the total gadgets by the number each box can hold.
117/13 = 9
Problem 2
A party has -117 guests and each table can seat 3 guests. How many tables are needed?
39 tables are needed.
Explanation
To find the number of tables required, divide the total guests by the number of guests each table can seat.
117/3 = 39
Problem 3
A library has 117 books to be distributed equally among 9 shelves. How many books will each shelf have?
Each shelf will have 13 books.
Explanation
To find the books on each shelf, divide the total books by the number of shelves.
117/9 = 13
Problem 4
In a competition, there are 117 participants, and they need to be divided into 13 teams. How many participants will be there in each team?
Each team will have 9 participants.
Explanation
Dividing the participants by the total teams will give the number of participants in each team.
117/13 = 9
Problem 5
A baker has 117 muffins and wants to arrange them equally in 3 trays. How many muffins will each tray have?
Each tray will have 39 muffins.
Explanation
Divide the total muffins by the number of trays.
117/3 = 39
FAQs on Factors of -117
1.What are the factors of -117?
2.Mention the prime factors of -117.
3.Is -117 a multiple of 9?
4.Mention the factor pairs of -117?
5.What is the absolute value of -117?
6.How can children in India use numbers in everyday life to understand Factors of -117?
7.What are some fun ways kids in India can practice Factors of -117 with numbers?
8.What role do numbers and Factors of -117 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of -117 skills?
Important Glossaries for Factors of -117
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -117 are -1, -3, -9, -13, -39, -117, 1, 3, 9, 13, 39, and 117.
- Prime factors: The factors which are prime numbers. For example, 3 and 13 are prime factors of 117.
- 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 117 are (1, 117), (3, 39), etc.
- Negative factors: Factors that are negative and divide the negative number without a remainder. For example, -1, -3, -9, etc., are negative factors of -117.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 117 is 3² × 13.
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About BrightChamps in India
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.
