

What are the Factor Pairs and Prime Factors of 125?
The concept of factors of 125 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Understanding factors allows students to break down numbers, work with multiplication and division, and analyze numerical patterns, especially with perfect cubes like 125.
Understanding Factors of 125
A factor of 125 is any whole number that divides 125 exactly, leaving no remainder. Factors are important in prime factorization, finding factor pairs, divisibility, and understanding number properties. For example, 1, 5, 25, and 125 are all whole numbers that can divide 125 evenly, so they are the factors of 125. Knowing the factors helps greatly with algebra, multiples, and simplifying math problems.
List of All Factors of 125
The factors of 125 are:
Each of these numbers divides 125 completely, without leaving a remainder.
Factors of 125 in Pairs
Factor pairs are two numbers that, when multiplied together, give 125. Here are both the positive and negative factor pairs of 125:
Pair | Product |
---|---|
(1, 125) | 1 × 125 = 125 |
(5, 25) | 5 × 25 = 125 |
(-1, -125) | (-1) × (-125) = 125 |
(-5, -25) | (-5) × (-25) = 125 |
This table makes it simple to spot all possible combinations that form 125.
Prime Factorization of 125
Prime factorization helps break a number into its smallest prime factor components. For 125, here is the step-by-step prime factorization:
2. Divide 25 by 5: 25 ÷ 5 = 5
3. Divide 5 by 5: 5 ÷ 5 = 1
So, the prime factorization of 125 is: 5 × 5 × 5 or \(5^3\).
This shows clearly that 125 is a perfect cube (since it is 5 × 5 × 5).
How to Find the Factors of 125 (Step-by-Step)
To find all the factors of 125 using the division method, follow these steps:
2. If the result is a whole number (no remainder), that divisor is a factor.
- 125 ÷ 1 = 125 ✔️
- 125 ÷ 2 = 62.5 (not whole, so skip)
- 125 ÷ 5 = 25 ✔️
- 125 ÷ 25 = 5 ✔️
- 125 ÷ 125 = 1 ✔️
3. Each quotient that is a whole number gives a factor. Thus, the factors are 1, 5, 25, 125.
Solved Example – Factor Related Question
Example: What is the sum of all factors of 125?
Step 2. Add them: 1 + 5 + 25 + 125 = 156
Related Numbers and Comparative Links
Studying the factors of 125 is easier when you compare them with similar numbers. Explore these for a deeper understanding:
- Factors of 25 – 25 is also a factor and a perfect square.
- Factors of 64 – Compare two different perfect cubes (125 and 64).
- Factors of 150 – See how 125 compares with nearby composite numbers.
- Factors of 105 – Practice with other three-digit factors.
- Prime Numbers – Revision of the concept for factorization.
- Factors of 100 – Compare perfect square (100) vs perfect cube (125).
- Multiples of 4 – Understand factors vs multiples.
- Factors and Multiples – Complete overview.
- Table of 125 – Visualize multiplication patterns for factor pairs.
- Factors of 12 – Practice with small composite numbers.
- Factors of 120 – Test divisibility rules with numbers close to 125.
- Factors of a Number – Master the division process for all numbers.
Practice Problems
- Write all the factors of 125 along with their pairs.
- Is 25 a factor of 125? Show the process.
- Find all perfect square factors of 125.
- Is 10 a factor of 125? Explain why or why not.
- List and compare factors of 125 and 25.
Common Mistakes to Avoid
- Confusing factors of 125 with multiples of 125 (factors are numbers that divide, not numbers that are divisible by 125).
- Forgetting to include 1 and 125 themselves as factors.
- Assuming every number less than 125 is a factor, which is never true.
Real-World Applications
The concept of factors of 125 can be used in sharing and packaging (like 125 items divided equally), in algebraic simplifications, and in competitive mathematics exams. Vedantu helps students approach such factorization problems with step-by-step logic, building confidence for exams and real applications.
We explored the idea of factors of 125, how to find them, how to factorize 125 into its prime factors, and where these concepts help in both academic and real-world math. For more practice, in-depth explanations and live problem solving, keep learning with Vedantu!
FAQs on Factors of 125 – List, Pairs, Prime Factorization & Methods
1. What are the factors of 125?
The factors of 125 are the numbers that divide it exactly without leaving any remainder. The factors of 125 are 1, 5, 25, and 125. These numbers multiply in pairs to give the product 125.
2. What is the prime factorization of 125?
The prime factorization of 125 is breaking it down into prime numbers that multiply to form 125. Since 125 = 5 × 5 × 5, its prime factors are 5, 5, and 5, or 53.
3. How do you find the factors of 125 using division?
To find factors of 125 using the division method, divide 125 by numbers starting from 1 up to 125. If the division results in a whole number with no remainder, then that divisor is a factor. For example, 125 ÷ 5 = 25 (no remainder), so 5 is a factor; similarly, 125 ÷ 25 = 5, so 25 is a factor.
4. What is the factor tree for 125?
A factor tree of 125 visually breaks down 125 into its prime factors by successive division. Starting with 125, divide by 5 to get 25, then divide 25 by 5 to get 5, and finally 5 by 5 to get 1. The factor tree shows 125 = 5 × 5 × 5.
5. What are the factor pairs of 125?
The factor pairs of 125 are the sets of two numbers that multiply to give 125. They are (1, 125) and (5, 25) for positive factors. Including negatives, the pairs are (-1, -125) and (-5, -25).
6. Which numbers is 125 divisible by?
125 is divisible by its factors: 1, 5, 25, and 125. This means 125 can be divided exactly by these numbers without leaving a remainder.
7. Why is 12 not a factor of 125?
12 is not a factor of 125 because dividing 125 by 12 does not give a whole number—it leaves a remainder. For a number to be a factor, it must divide the original number exactly with no remainder.
8. Why do students confuse factors with multiples of 125?
Students often confuse factors and multiples because both relate to division and multiplication. However, factors of 125 are numbers that divide 125 exactly, while multiples of 125 are numbers obtained by multiplying 125 with whole numbers. Understanding this distinction is key to avoiding confusion.
9. Why is 125 called a perfect cube but not a perfect square?
125 is called a perfect cube because it can be expressed as 5 × 5 × 5, or 53. It is not a perfect square because it cannot be expressed as the product of a number multiplied by itself (n × n). In other words, there is no whole number whose square is 125.
10. Why can only positive numbers be factors in this list?
Positive numbers are generally considered when listing factors because factors represent the building blocks to multiply and get the original positive number. While negative numbers can technically be factors (since a negative × a negative = positive), most educational content focuses on positive factors for simplicity and clarity.
11. How are factor pairs helpful in solving quadratic problems?
Factor pairs are essential in quadratic problems because they help find two numbers whose product equals the constant term and whose sum equals the coefficient of the middle term. Understanding factor pairs of numbers like 125 can aid in breaking down and solving such equations more efficiently.
12. What is the sum of all factors of 125?
The sum of all factors of 125 is calculated by adding 1 + 5 + 25 + 125 = 156. This sum can be used in various problems involving divisibility and factorization.

















