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 -12, how they are used in real life, and tips to learn them quickly.
The numbers that divide -12 evenly are known as factors of -12.
A factor of -12 is a number that divides the number without remainder.
The factors of -12 are 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, and -12.
Prime factors of 12: 2 and 3.
Prime factorization of 12: 2² × 3.
The sum of the positive factors of 12: 1 + 2 + 3 + 4 + 6 + 12 = 28.
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 -12. Identifying the numbers which are multiplied to get the number -12 is the multiplication method.
Step 1: Multiply -12 by 1, -12 × 1 = -12.
Step 2: Check for other numbers that give -12 after multiplying:
-1 × 12 = -12
-2 × 6 = -12
-3 × 4 = -12
Therefore, the positive factor pairs of 12 are: (1, 12), (2, 6), (3, 4).
For every positive factor pair, there is a negative counterpart, such as (-1, -12), (-2, -6), (-3, -4).
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 -12 by 1, -12 ÷ 1 = -12.
Step 2: Continue dividing -12 by the numbers until the remainder becomes 0.
-12 ÷ 1 = -12
-12 ÷ 2 = -6
-12 ÷ 3 = -4
-12 ÷ 4 = -3
-12 ÷ 6 = -2
-12 ÷ 12 = -1
Therefore, the factors of -12 are: 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, -12.
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 12 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
The prime factors of 12 are 2 and 3.
The prime factorization of 12 is: 2² × 3.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 12 is divided by 2 to get 6.
Step 2: Now divide 6 by 2 to get 3.
Step 3: 3 is a prime number and cannot be divided further.
So, the prime factorization of 12 is: 2² × 3.
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 12: (1, 12), (2, 6), (3, 4).
Negative factor pairs of -12: (-1, -12), (-2, -6), (-3, -4).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 3 teams and -12 points. If points are to be distributed equally, how many points will each team receive?
Each team will receive -4 points.
To distribute the points equally, we need to divide the total points by the number of teams.
-12/3 = -4
A company has a debt of -12 million dollars and wants to pay it off in 6 equal installments. How much will each installment be?
Each installment will be -2 million dollars.
To find each installment, divide the total debt by the number of installments.
-12/6 = -2
A group of 4 players has a score of -12. How will the score be distributed among them equally?
Each player will have a score of -3.
To distribute the score equally, divide the total score by the number of players.
-12/4 = -3
If a loss of -12 dollars is shared among 2 partners equally, how much does each partner bear?
Each partner bears -6 dollars.
Dividing the total loss by the number of partners gives the loss per partner.
-12/2 = -6
A group of 6 hikers shares a debt of -12 dollars. How much debt does each hiker have?
Each hiker has -2 dollars in debt.
Divide the total debt by the number of hikers.
-12/6 = -2
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.