102 LearnersLast updated on May 26th, 2025
Factors of -75
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 -75, how they are used in real life, and tips to learn them quickly.
What are the Factors of -75?
The numbers that divide -75 evenly are known as factors of -75.
A factor of -75 is a number that divides the number without a remainder.
The factors of -75 are 1, 3, 5, 15, 25, and 75.
Negative factors of -75: -1, -3, -5, -15, -25, and -75.
Prime factors of -75: 3 and 5.
Prime factorization of -75: -1 × 3 × 5².
The sum of the positive factors of 75: 1 + 3 + 5 + 15 + 25 + 75 = 124
How to Find Factors of -75?
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 -75. Identifying the numbers which are multiplied to get the number -75 is the multiplication method.
Step 1: Multiply -75 by 1, -75 × 1 = -75.
Step 2: Check for other numbers that give -75 after multiplying 3 × -25 = -75 5 × -15 = -75
Therefore, the positive factor pairs of -75 are: (1, -75), (3, -25), and (5, -15).
For every positive factor, there is a corresponding 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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide -75 by 1, -75 ÷ 1 = -75.
Step 2: Continue dividing -75 by the numbers until the remainder becomes 0.
-75 ÷ 1 = -75
-75 ÷ 3 = -25
-75 ÷ 5 = -15
Therefore, the factors of -75 are: 1, 3, 5, 15, 25, and 75.
Prime Factors and Prime Factorization
The factors can be found by dividing them with a prime number. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of -75 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
-75 ÷ -1 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of -75 are 3 and 5.
The prime factorization of -75 is: -1 × 3 × 5².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, -75 is divided by -1 to get 75.
Step 2: Now divide 75 by 3 to get 25.
Step 3: Then divide 25 by 5 to get 5. Here, 5 is a prime number that cannot be divided anymore.
So, the prime factorization of -75 is: -1 × 3 × 5².
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 -75: (1, -75), (3, -25), and (5, -15).
Negative factor pairs of -75: (-1, 75), (-3, 25), and (-5, 15).
Common Mistakes and How to Avoid Them in Factors of -75
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 -75, 1 and -75 are also factors.
Factors of -75 Examples
Problem 1
A box contains -75 marbles, and you are asked to divide them into 5 equal groups. How many marbles will be in each group?
Each group will have -15 marbles.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of groups.
-75/5 = -15
Problem 2
A recipe requires -75 grams of an ingredient, and you have 15 packets. How much does each packet weigh?
Each packet weighs -5 grams.
Explanation
To find the weight of each packet, divide the total weight by the number of packets.
-75/15 = -5
Problem 3
A machine needs to produce -75 parts, and it operates in cycles of 3 parts. How many cycles are required?
25 cycles are required.
Explanation
To find the number of cycles, divide the total parts by parts per cycle.
-75/(-3) = 25
Problem 4
You have -75 meters of fabric and need to cut it into pieces of 25 meters each. How many pieces can you cut?
You can cut 3 pieces.
Explanation
Dividing the total fabric by the length of each piece gives the number of pieces.
-75/25 = -3
Problem 5
A company has a debt of -75 dollars and wants to repay it in 5 installments. How much is each installment?
Each installment is -15 dollars.
Explanation
Divide the total debt by the number of installments.
-75/5 = -15
FAQs on Factors of -75
1.What are the factors of -75?
2.Mention the prime factors of -75.
3.Is -75 a multiple of 5?
4.Mention the factor pairs of -75?
5.What is the square of -75?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of -75?
7.What are some fun ways kids in Saudi Arabia can practice Factors of -75 with numbers?
8.What role do numbers and Factors of -75 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of -75 skills?
Important Glossaries for Factors of -75
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -75 are 1, 3, 5, 15, 25, and 75.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of -75.
- 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 -75 are (1, -75), (3, -25), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of -75 is -1 × 3 × 5².
- Negative factors: These are factors of a number that are negative. For example, the negative factors of -75 are -1, -3, -5, -15, -25, and -75.
Explore More numbers
Previous to Factors of -75
About BrightChamps in Saudi Arabia
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.
