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 -45, how they are used in real life, and tips to learn them quickly.
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
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 -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.
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.
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 -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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To divide the compost equally, we need to divide the total compost by the number of sections.
-45/5 = -9
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.
To find the monthly loss, we divide the total loss by the number of months.
-45/3 = -15
A baker needs to distribute -45 cupcakes into 9 boxes. How many cupcakes go into each box?
Each box will have -5 cupcakes.
To find the cupcakes in each box, divide the total cupcakes by the number of boxes.
-45/9 = -5
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.
Dividing the debt with the number of workers, we will get each worker's share.
-45/15 = -3
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.
Divide total penalty points by the number of students.
-45/45 = -1
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.