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 items equally, arranging things, etc. In this topic, we will learn about the factors of -105, how they are used in real life, and the tips to learn them quickly.
The numbers that divide -105 evenly are known as factors of -105.
A factor of -105 is a number that divides the number without remainder.
The factors of -105 are 1, 3, 5, 7, 15, 21, 35, and 105.
Negative factors of -105: -1, -3, -5, -7, -15, -21, -35, and -105.
Prime factors of -105: 3, 5, and 7.
Prime factorization of -105: -1 × 3 × 5 × 7.
The sum of factors of 105: 1 + 3 + 5 + 7 + 15 + 21 + 35 + 105 = 192
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 -105. Identifying the numbers which are multiplied to get the number -105 is the multiplication method.
Step 1: Multiply -105 by 1, -105 × 1 = -105.
Step 2: Check for other numbers that give -105 after multiplying
3 × -35 = -105
5 × -21 = -105
7 × -15 = -105
Therefore, the positive factor pairs of -105 are: (1, -105), (3, -35), (5, -21), (7, -15).
For every positive factor, there is a negative factor.
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 -105 by 1, -105 ÷ 1 = -105.
Step 2: Continue dividing -105 by the numbers until the remainder becomes 0.
-105 ÷ 1 = -105
-105 ÷ 3 = -35
-105 ÷ 5 = -21
-105 ÷ 7 = -15
Therefore, the factors of -105 are: 1, 3, 5, 7, 15, 21, 35, 105.
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 -105 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-105 ÷ -1 = 105
105 ÷ 3 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of -105 are 3, 5, and 7.
The prime factorization of -105 is: -1 × 3 × 5 × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, -105 is divided by -1 to get 105.
Step 2: Now divide 105 by 3 to get 35.
Step 3: Then divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -105 is: -1 × 3 × 5 × 7.
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 -105: (1, -105), (3, -35), (5, -21), and (7, -15).
Negative factor pairs of -105: (-1, 105), (-3, 35), (-5, 21), and (-7, 15).
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 group of 5 friends has -105 points, how many points did each friend lose if divided equally?
Each friend lost 21 points.
To divide the points equally, we need to divide the total points by the number of friends.
-105/5 = -21
A loss of -105 dollars is to be shared among 7 investors equally. How much loss does each investor bear?
Each investor bears a loss of 15 dollars.
To find the loss per investor, we divide the total loss by the number of investors.
-105/7 = -15
A game has -105 penalty points to be distributed among 3 players. How many penalty points does each player get?
Each player gets 35 penalty points.
To find the penalty points per player, divide the total penalty points by the number of players.
-105/3 = -35
A team lost -105 goals over 15 matches. How many goals did they lose per match?
They lost 7 goals per match.
Dividing the total goals lost by the number of matches gives us the goals lost per match.
-105/15 = -7
A company has a debt of -105 dollars spread over 21 months. What is the monthly debt?
The monthly debt is 5 dollars.
Divide the total debt by the number of months to find the monthly debt.
-105/21 = -5
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.