123 LearnersLast updated on May 26th, 2025
Factors of -125
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 -125, how they are used in real life, and tips to learn them quickly.
What are the Factors of -125?
The numbers that divide -125 evenly are known as factors of -125.
A factor of -125 is a number that divides the number without remainder.
The factors of -125 are 1, 5, 25, and 125.
Negative factors of -125: -1, -5, -25, and -125.
Prime factors of 125: 5. Prime factorization of 125: 5³.
The sum of factors of -125: 1 + 5 + 25 + 125 = 156
How to Find Factors of -125?
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 125. Identifying the numbers that are multiplied to get the number 125 is the multiplication method.
Step 1: Multiply 125 by 1, 125 × 1 = 125.
Step 2: Check for other numbers that give 125 after multiplying 5 × 25 = 125
Therefore, the positive factor pairs of 125 are: (1, 125), (5, 25).
All these factor pairs result in 125.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 125 by 1, 125 ÷ 1 = 125.
Step 2: Continue dividing 125 by the numbers until the remainder becomes 0.
125 ÷ 1 = 125
125 ÷ 5 = 25
125 ÷ 25 = 5
Therefore, the factors of 125 are: 1, 5, 25, 125.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 125 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factor of 125 is 5. The prime factorization of 125 is: 5³.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 125 is divided by 5 to get 25.
Step 2: Now divide 25 by 5 to get 5. Step 3: Divide 5 by 5 to get 1. Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 125 is: 5³.
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 125: (1, 125), (5, 25).
Negative factor pairs of 125: (-1, -125), (-5, -25).
Common Mistakes and How to Avoid Them in Factors of -125
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 125, 1 and 125 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, and always check whether you have mentioned negative factors.
For example, the factors of 125 include -1, -5, -25, 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 125/1.5 = 83.333, 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 125 are prime numbers.
For example, 5 is the prime factor of 125, but it has other factors like 25, 125.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 125 as 5³ and missing all the key factors.
Factors of -125 Examples
Problem 1
There are 5 students and 125 chocolates. How will they divide them equally?
They will get 25 chocolates each.
Explanation
To divide the chocolates equally, we need to divide the total chocolates by the number of students.
125/5 = 25
Problem 2
A block is cubic, with each side measuring 5 meters, and the total volume is 125 cubic meters. What is the height?
5 meters.
Explanation
To find the height of the block, we use the formula, Volume = side × side × height 125 = 5 × 5 × height
To find the value of height, we need to shift 5² to the left side.
125/25 = height
Height = 5.
Problem 3
There are 25 gift boxes and 125 candies. How many candies will be in each box?
Each box will have 5 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
125/25 = 5
Problem 4
In a club, there are 125 members, and 5 groups. How many members are there in each group?
There are 25 members in each group.
Explanation
Dividing the members by the total groups, we will get the number of members in each group.
125/5 = 25
Problem 5
125 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each shelf has 25 books.
Explanation
Divide total books by shelves.
125/5 = 25
FAQs on Factors of -125
1.What are the factors of -125?
2.Mention the prime factors of 125.
3.Is 125 a multiple of 5?
4.Mention the factor pairs of 125?
5.What is the cube of 125?
Important Glossaries for Factor of -125
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 125 are 1, 5, 25, and 125.
- Prime factors: The factors which are prime numbers. For example, 5 is a prime factor of 125.
- Negative factors: Factors that are negative counterparts of positive factors. For example, -1, -5, -25, -125.
- 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 125 are (1, 125), (5, 25).
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 125 is expressed as 5³.
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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.
