Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To find the number of boxes, divide the total gadgets by the number each box can hold.
117/13 = 9
A party has -117 guests and each table can seat 3 guests. How many tables are needed?
39 tables are needed.
To find the number of tables required, divide the total guests by the number of guests each table can seat.
117/3 = 39
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.
To find the books on each shelf, divide the total books by the number of shelves.
117/9 = 13
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.
Dividing the participants by the total teams will give the number of participants in each team.
117/13 = 9
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.
Divide the total muffins by the number of trays.
117/3 = 39
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.
: She loves to read number jokes and games.