126 LearnersLast updated on May 26th, 2025
Factors of -189
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.
What are the Factors of -189?
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.
How to Find Factors of -189?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 -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.
Finding Factors Using Division Method
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.
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 -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.
Factor Tree
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).
Common Mistakes and How to Avoid Them in Factors of -189
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 number. Always remember to include 1 and the number itself.
For example, in factors of -189, 1 and -189 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -189 consist of -1, -3, -7, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because -189/1.5 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 -189 are prime numbers. While 3 and 7 are the prime factors of -189, it has other factors like 9, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -189 as -1 × 3³ × 7 and missing all the key factors.
Factors of -189 Examples
Problem 1
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.
Explanation
To distribute the points equally, divide the total points by the number of teams.
-189/9 = -21
Problem 2
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.
Explanation
To find the number of pieces, divide the total length by the length of each piece.
189/7 = 27
Problem 3
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.
Explanation
To find the number of paintings in each wing, divide the total paintings by the wings.
-189/3 = -63
Problem 4
There are 27 boxes and -189 items. How many items will be in each box?
Each box will have -7 items.
Explanation
Dividing the items by the total boxes, we will get the number of items in each box.
-189/27 = -7
Problem 5
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.
Explanation
Divide the total seats by rows.
-189/21 = -9
FAQs on Factors of -189
1.What are the factors of -189?
2.Mention the prime factors of -189.
3.Is -189 a multiple of 9?
4.Mention the factor pairs of -189?
5.What is the absolute value of -189?
6.How can children in Oman use numbers in everyday life to understand Factors of -189?
7.What are some fun ways kids in Oman can practice Factors of -189 with numbers?
8.What role do numbers and Factors of -189 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of -189 skills?
Important Glossaries for Factors of -189
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -189 are 1, 3, 7, 9, 21, 27, 63, and 189.
- Prime factors: The factors which are prime numbers. For example, 3 and 7 are prime factors of -189.
- 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 -189 are (1, -189), (3, -63), etc.
- Multiplication method: A technique used to find factors by identifying pairs of numbers that multiply to give a specific number.
- Division method: A technique used to find factors by dividing a number by various whole numbers to see which divisions yield no remainder.
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About BrightChamps in Oman
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
: She loves to read number jokes and games.
