123 LearnersLast updated on May 26th, 2025
Factors of -45
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 -45, how they are used in real life, and tips to learn them quickly.
What are the Factors of -45?
The numbers that divide -45 evenly are known as factors of -45.
A factor of -45 is a number that divides the number without remainder.
The factors of -45 are 1, 3, 5, 9, 15, and 45.
Negative factors of -45: -1, -3, -5, -9, -15, and -45.
Prime factors of -45: 3 and 5.
Prime factorization of -45: -1 × 3 × 3 × 5.
The sum of factors of -45: 1 + 3 + 5 + 9 + 15 + 45 = 78
How to Find Factors of -45?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 -45. Identifying the numbers which are multiplied to get the number -45 is the multiplication method.
Step 1: Multiply -45 by 1, -45 × 1 = -45.
Step 2: Check for other numbers that give -45 after multiplying 3 × -15 = -45 5 × -9 = -45
Therefore, the positive factor pairs of -45 are: (1, -45), (3, -15), (5, -9).
All these factor pairs result in -45.
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 -45 by 1, -45 ÷ 1 = -45.
Step 2: Continue dividing -45 by the numbers until the remainder becomes 0.
-45 ÷ 1 = -45
-45 ÷ 3 = -15
-45 ÷ 5 = -9
-45 ÷ 9 = -5
-45 ÷ 15 = -3
Therefore, the factors of -45 are: 1, 3, 5, 9, 15, 45.
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 -45 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-45 ÷ 3 = -15
-15 ÷ 3 = -5
-5 ÷ 5 = -1
The prime factors of -45 are 3 and 5.
The prime factorization of -45 is: -1 × 3 × 3 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, -45 is divided by 3 to get -15.
Step 2: Now divide -15 by 3 to get -5.
Step 3: Divide -5 by 5 to get -1. Here, -1 is the smallest number that cannot be divided anymore.
So, the prime factorization of -45 is: -1 × 3 × 3 × 5.
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 -45: (1, -45), (3, -15), (5, -9).
Negative factor pairs of -45: (-1, 45), (-3, 15), (-5, 9).
Common Mistakes and How to Avoid Them in Factors of -45
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 word. Always remember to include 1 and the number itself.
For example, in factors of -45, 1 and -45 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 -45 consist of -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -45/1.5 = -30, and it 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 -45 are prime numbers.
For example, 3 and 5 are the prime factors of -45, but it has other factors like 9, 15.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -45 as -1 × 3 × 3 × 5 and missing all the key factors.
Factors of -45 Examples
Problem 1
A farmer wants to equally distribute -45 kilograms of compost among 5 sections of his garden. How much compost does each section receive?
Each section receives -9 kilograms of compost.
Explanation
To divide the compost equally, we need to divide the total compost by the number of sections.
-45/5 = -9
Problem 2
A company incurs a loss of -45 dollars equally over 3 months. What is the loss per month?
The company incurs a loss of -15 dollars per month.
Explanation
To find the monthly loss, we divide the total loss by the number of months.
-45/3 = -15
Problem 3
A baker needs to distribute -45 cupcakes into 9 boxes. How many cupcakes go into each box?
Each box will have -5 cupcakes.
Explanation
To find the cupcakes in each box, divide the total cupcakes by the number of boxes.
-45/9 = -5
Problem 4
A contractor evenly splits a debt of -45 units among 15 workers. What is each worker's share?
Each worker's share is -3 units.
Explanation
Dividing the debt with the number of workers, we will get each worker's share.
-45/15 = -3
Problem 5
A teacher divides a penalty of -45 points equally among 45 students. How many points are deducted per student?
Each student has -1 point deducted.
Explanation
Divide total penalty points by the number of students.
-45/45 = -1
FAQs on Factors of -45
1.What are the factors of -45?
2.Mention the prime factors of -45.
3.Is -45 a multiple of 5?
4.Mention the factor pairs of -45?
5.What is the square of -45?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of -45?
7.What are some fun ways kids in United Kingdom can practice Factors of -45 with numbers?
8.What role do numbers and Factors of -45 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of -45 skills?
Important Glossaries for Factor of -45
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -45 are 1, 3, 5, 9, 15, and 45.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of -45.
- 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 -45 are (1, -45), (3, -15), etc.
- Negative factors: These are factors of a negative number that are negative themselves. For example, the negative factors of -45 are -1, -3, -5, etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of -45 is -1 × 3 × 3 × 5.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of -45
About BrightChamps in United Kingdom
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.
