Factors of 50 and How to Find Them: A Detailed Guide
What are Factors?
Factors are numbers that divide another number exactly, leaving no remainder. For example, the factors of 50 include 1, 2, 5, 10, 25, and 50.
The number 50 is a milestone number in many aspects of life and mathematics. Known for its even divisibility and interesting properties, 50 serves as a great example to explore the concept of factors. This guide will delve into the factors of 50 and explain how to find them. Explore the factors of 50 in this comprehensive guide. Learn how to find factors, understand prime factorization, and discover the unique properties of the number 50.
Factors of 50:
The complete list of factors for 50 is:
- 1, 2, 5, 10, 25, 50.

Prime Factors of 50:
Prime factors are prime numbers that divide a given number exactly. The prime factors of 50 are:
- 2 and 5.
Proper Factors:
Proper factors exclude the number itself and 1. For 50, the proper factors are:
- 2, 5, 10, 25.
Factor Pairs:
Factors come in pairs that multiply to give the original number. The factor pairs of 50 are:
- (1, 50), (2, 25), and (5, 10).

How to Find Factors:
To find the factors of 50:
- Start with 1 and 50.
- Check divisibility for each number up to the square root of 50.
- Record all numbers that divide 50 exactly.
Prime Factorization:
Prime factorization breaks down a number into its prime factors:
- For 50: 50 = 2 × 5 × 5, which simplifies to 50 = 2 × 5².
Special Properties of 50:
50 is an even number and a composite number. It is also significant in various cultural contexts, such as the number of states in the USA and the number of years in a golden anniversary.
Comparison Table of Factors:
Number | Factors | Prime Factors | Proper Factors |
---|---|---|---|
6 | 1, 2, 3, 6 | 2, 3 | 2, 3 |
18 | 1, 2, 3, 6, 9, 18 | 2, 3 | 2, 3, 6, 9 |
50 | 1, 2, 5, 10, 25, 50 | 2, 5 | 2, 5, 10, 25 |
Solved Examples
Example 1:
Question: There are 50 pencils distributed equally in 5 boxes. How many pencils are there in total?
Solution:
- Total number of pencils = 50
- Number of boxes = 5
- Number of pencils in each box = 50 ÷ 5 = 10
Therefore, each box has 10 pencils.
Example 2:
Question: The price of one mango is Rs. 5. What will be the total cost for 10 mangoes?
Solution:
- Price of one mango = Rs. 5
- Price of 10 mangoes = 10 × 5 = Rs. 50
Hence, the total cost of 10 mangoes is Rs. 50.
Example 3:
Question: What are the common factors of 50 and 100?
Solution:
- Factors of 50 = 1, 2, 5, 10, 25, 50
- Factors of 100 = 1, 2, 5, 10, 20, 25, 50, 100
The common factors of 50 and 100 are 1, 2, 5, 10, 25, and 50.
Frequently Asked Questions (FAQs)
Q1: What are the factors of 50?
The factors of 50 are natural numbers that can divide 50 without leaving a remainder. They are 1, 2, 5, 10, 25, and 50.
Q2: Are factors and multiples of 50 the same?
No, they are different. Factors divide the number into equal parts, while multiples are obtained by multiplying 50 by natural numbers.
Q3: What are the multiples of 50?
The first 10 multiples of 50 are: 50, 100, 150, 200, 250, 300, 350, 400, 450, and 500.
Q4: What is the largest prime factor of 50?
The prime factorization of 50 is 2 × 5 × 5, so the largest prime factor is 5.
Q5: What are the common factors of 50, 125, and 150?
Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 125: 1, 5, 25, 125
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
The common factors of 50, 125, and 150 are 1, 5, and 25.
Conclusion:
Understanding the factors of 50 provides insight into its mathematical properties and significance. Whether you’re a student or an enthusiast, practicing factorization with different numbers enhances your number theory skills. Dive into the world of numbers and explore the fascinating properties they hold!