Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without a 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 -189, how they are used in real life, and tips to learn them quickly.
The numbers that divide -189 evenly are known as factors of -189.
A factor of -189 is a number that divides the number without remainder.
The factors of -189 are 1, 3, 7, 9, 21, 27, 63, and 189.
Negative factors of -189: -1, -3, -7, -9, -21, -27, -63, and -189.
Prime factors of -189: 3 and 7.
Prime factorization of -189: -1 × 3³ × 7.
The sum of the positive factors of 189: 1 + 3 + 7 + 9 + 21 + 27 + 63 + 189 = 320.
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 -189. Identifying the numbers which are multiplied to get the number -189 is the multiplication method.
Step 1: Multiply -189 by -1, -189 × -1 = 189.
Step 2: Check for other numbers that give -189 after multiplying:
3 × -63 = -189
7 × -27 = -189
9 × -21 = -189
Therefore, the positive factor pairs of -189 are: (1, -189), (3, -63), (7, -27), (9, -21).
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 a simple division method
Step 1: Divide -189 by 1, -189 ÷ 1 = -189.
Step 2: Continue dividing -189 by the numbers until the remainder becomes 0.
-189 ÷ 1 = -189
-189 ÷ 3 = -63
-189 ÷ 7 = -27
-189 ÷ 9 = -21
Therefore, the factors of -189 are: 1, 3, 7, 9, 21, 27, 63, 189.
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 -189 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-189 ÷ -1 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of -189 are 3 and 7.
The prime factorization of -189 is: -1 × 3³ × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 189 is divided by 3 to get 63.
Step 2: Now divide 63 by 3 to get 21.
Step 3: Then divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of -189 is: -1 × 3³ × 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 -189: (1, -189), (3, -63), (7, -27), and (9, -21).
Negative factor pairs of -189: (-1, 189), (-3, 63), (-7, 27), and (-9, 21).
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 9 teams, and -189 points need to be distributed evenly among them. How many points will each team receive?
Each team will receive -21 points.
To distribute the points equally, divide the total points by the number of teams.
-189/9 = -21
A rope is 189 meters long and needs to be cut into equal pieces of 7 meters each. How many pieces will there be?
27 pieces.
To find the number of pieces, divide the total length by the length of each piece.
189/7 = 27
An art gallery has -189 paintings that need to be displayed in 3 wings. How many paintings will be in each wing?
Each wing will have -63 paintings.
To find the number of paintings in each wing, divide the total paintings by the wings.
-189/3 = -63
There are 27 boxes and -189 items. How many items will be in each box?
Each box will have -7 items.
Dividing the items by the total boxes, we will get the number of items in each box.
-189/27 = -7
A theater has 21 rows and needs to arrange -189 seats. How many seats will be in each row?
Each row will have -9 seats.
Divide the total seats by rows.
-189/21 = -9
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.