119 LearnersLast updated on May 26th, 2025
Factors of -162
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 -162, how they are used in real life, and tips to learn them quickly.
What are the Factors of -162?
The numbers that divide -162 evenly are known as factors of -162.
A factor of -162 is a number that divides the number without a remainder.
The factors of -162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.
Negative factors of -162: -1, -2, -3, -6, -9, -18, -27, -54, -81, and -162.
Prime factors of -162: 2 and 3.
Prime factorization of -162: 2 × 34.
The sum of the positive factors of 162 is 1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 + 81 + 162 = 363.
How to Find Factors of -162?
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 162. Identifying the numbers that are multiplied to get the number 162 is the multiplication method.
Step 1: Multiply 162 by 1, 162 × 1 = 162.
Step 2: Check for other numbers that give 162 after multiplying 2 × 81 = 162 3 × 54 = 162 6 × 27 = 162 9 × 18 = 162
Therefore, the positive factor pairs of 162 are: (1, 162), (2, 81), (3, 54), (6, 27), (9, 18).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the 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 162 by 1, 162 ÷ 1 = 162.
Step 2: Continue dividing 162 by the numbers until the remainder becomes 0.
162 ÷ 1 = 162
162 ÷ 2 = 81
162 ÷ 3 = 54
162 ÷ 6 = 27
162 ÷ 9 = 18
Therefore, the factors of -162 are: 1, 2, 3, 6, 9, 18, 27, 54, 81, 162.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. 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 162 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
162 ÷ 2 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 162 are 2 and 3.
The prime factorization of 162 is: 2 × 3^4.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 162 is divided by 2 to get 81.
Step 2: Now divide 81 by 3 to get 27.
Step 3: Then divide 27 by 3 to get 9.
Step 4: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 162 is: 2 × 34.
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 162: (1, 162), (2, 81), (3, 54), (6, 27), and (9, 18).
Negative factor pairs of -162: (-1, -162), (-2, -81), (-3, -54), (-6, -27), and (-9, -18).
Common Mistakes and How to Avoid Them in Factors of -162
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 -162, 1 and 162 is also a factor.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of -162 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 162/1.5 does not result in 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 -162 are prime numbers.
For example, 2 and 3 are the prime factors of 162, but it has other factors like 6, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 162 as 2 × 3^4 and missing all the key factors.
Factors of -162 Examples
Problem 1
There are 9 friends and 162 candies. How will they divide it equally?
They will get 18 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
162/9 = 18
Problem 2
A field is rectangular, the length of the field is 9 meters and the total area is 162 square meters. Find the width?
18 meters.
Explanation
To find the width of the field, we use the formula
Area = length × width
162 = 9 × width
To find the value of width, we need to shift 9 to the left side.
162/9 = width
Width = 18.
Problem 3
There are 27 gift bags and 162 candies. How many candies will be in each bag?
Each bag will have 6 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
162/27 = 6
Problem 4
In a class, there are 162 students, and 9 groups. How many students are there in each group?
There are 18 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
162/9 = 18
Problem 5
162 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 54 books.
Explanation
Divide total books with shelves.
162/3 = 54
FAQs on Factors of -162
1.What are the factors of -162?
2.Mention the prime factors of 162.
3.Is 162 a multiple of 9?
4.Mention the factor pairs of -162?
5.What is the square of 162?
Important Glossaries for Factor of -162
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 162.
- 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 162 are (1, 162), (2, 81), etc.
- Negative factors: Factors that are negative numbers dividing the given number without a remainder. For example, the negative factors of -162 include -1, -2, -3, etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 162 is 2 × 3^4.
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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.
