129 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 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 remainder. The factors of 117 are 1, 3, 9, 13, 39, and 117.
Negative factors of 117: -1, -3, -9, -13, -39, and -117.
Prime factors of 117: 3 and 13.
Prime factorization of 117: 3² × 13.
The sum of factors of 117: 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 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 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 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.
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 till 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 word. 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 a factor. Only whole numbers can be a factor. For example, thinking 1.5 as a factor because 117/1.5 = 78, 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 117 are prime numbers. For example, 3 and 13 are the prime factors of 117, but it has other factors like 9, 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
There are 13 students and 117 apples. How will they divide them equally?
They will get 9 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of students.
117/13 = 9
Problem 2
A plot is rectangular, and the length of the plot is 9 meters with a total area of 117 square meters. Find the width.
13 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
117 = 9 × width
To find the value of width, we need to shift 9 to the left side.
117/9 = width
Width = 13.
Problem 3
There are 39 gift bags and 117 candies. How many candies will be in each bag?
Each bag will have 3 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
117/39 = 3
Problem 4
In a class, there are 117 students, and 3 sections. How many students are there in each section?
There are 39 students in each section.
Explanation
Dividing the students with the total sections, we will get the number of students in each section.
117/3 = 39
Problem 5
117 books need to be distributed in 9 classrooms. How many books will go to each classroom?
Each classroom will receive 13 books.
Explanation
Divide total books with classrooms.
117/9 = 13
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 square of 117?
6.How can children in Australia use numbers in everyday life to understand Factors of 117?
7.What are some fun ways kids in Australia can practice Factors of 117 with numbers?
8.What role do numbers and Factors of 117 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia 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, 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.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the target number.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, 117 = 3² × 13.
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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
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