What are the factor pairs and prime factors of 50?
The concept of factors of 50 is an essential building block in mathematics, helping students understand how numbers break down and how they are used in calculations and problem-solving. Learning about the factors of 50 will help you in topics like multiples, prime factorization, and finding highest common factors, both in exams and in everyday life.
What Is Factors of 50?
A factor of 50 is any whole number that can divide 50 exactly, leaving no remainder. In other words, when you multiply two whole numbers and the product is 50, both numbers are factors. You’ll find this concept applied when solving problems involving prime factorization, LCM and HCF, and even when working with multiples and divisors in daily calculations.
Key Formula for Factors of 50
Here’s the standard formula for finding the number of factors using prime factorization:
If \( 50 = 2^1 \times 5^2 \), then the total number of factors = (1+1) × (2+1) = 2 × 3 = 6.
How to Find Factors of 50
To list out all factors of 50, you need to find all whole numbers that divide 50 without leaving a remainder.
- Start with 1: 50 ÷ 1 = 50 (so, 1 is a factor)
- Test 2: 50 ÷ 2 = 25 (so, 2 is a factor)
- Test 3: 50 ÷ 3 ≈ 16.67 (not a whole number, skip)
- Test 4: 50 ÷ 4 = 12.5 (not a whole number, skip)
- Test 5: 50 ÷ 5 = 10 (so, 5 and 10 are factors)
- Continue up to 50. (All whole numbers tried up to √50 are enough, as the factors repeat in pairs.)
- Don't forget 25 and 50 themselves!
Complete List of Factors and Factor Pairs
There are exactly six positive factors of 50. Here is an easy-to-read table:
| Factor | Pair Factor |
|---|---|
| 1 | 50 |
| 2 | 25 |
| 5 | 10 |
| 10 | 5 |
| 25 | 2 |
| 50 | 1 |
All factors of 50: 1, 2, 5, 10, 25, 50
Prime Factorization of 50
To write 50 as a product of prime numbers, use the division method:
1. Divide by 2 (smallest prime): 50 ÷ 2 = 252. 25 isn’t divisible by 2, try the next prime (3). 25 ÷ 3 = not exact.
3. Try 5 (next prime): 25 ÷ 5 = 5
4. 5 ÷ 5 = 1
So, the prime factors of 50 are 2 × 5 × 5, or \( 2^1 \times 5^2 \).
Exponential Form: 50 = 2¹ × 5²
Common Mistakes to Avoid
- Confusing factors with multiples (e.g., thinking 100 is a factor of 50—it’s not; 50 is a factor of 100).
- Missing out factor pairs completely by not checking divisibility beyond 1 and 2.
- Assuming “prime factors” are the same as all factors. (Prime factors are only those that are prime numbers; all factors include both composite and prime numbers.)
Solved Example Problems
Example 1: Is 8 a factor of 50?
1. Divide 50 by 8: 50 ÷ 8 = 6.25
2. 6.25 is not a whole number, so 8 is not a factor.
Example 2: Find the sum of all factors of 50.
1. List out all factors: 1, 2, 5, 10, 25, 50
2. Add them up: 1+2+5+10+25+50 = 93
3. Total sum = 93
Example 3: What is the prime factorization of 50 in exponential form?
1. 50 ÷ 2 = 25
2. 25 ÷ 5 = 5
3. 5 ÷ 5 = 1
4. So: 50 = 2 × 5 × 5 = 21 × 52
Factors vs Multiples
| Factors of 50 | Multiples of 50 |
|---|---|
| Numbers that divide 50 exactly Eg: 1, 2, 5, 10, 25, 50 |
Numbers you get by multiplying 50 by whole numbers Eg: 50, 100, 150, 200, ... |
Connection to Other Maths Numbers
Understanding 50’s factors helps when comparing with similar numbers:
- Factors of 48 – near 50, more factors due to more prime divisors.
- Factors of 60 – a highly composite number, good for comparison.
- Factors of 100 – double of 50, helps in understanding factor relationships.
Speed Trick or Vedic Shortcut
Need to spot factors of numbers like 50 quickly in a test?
Trick: For any number ending in 0, it is always divisible by 1, 2, 5, and 10. So, check for these first when finding factors.
Try These Yourself
- List all even factors of 50.
- Check if 25 is a multiple or a factor of 50.
- Find the common factors of 50 and 100.
- List all factors of 50 greater than 5.
Relation to Other Concepts
The idea of factors of 50 connects closely with factors of a number in general, and prime factorization, making it useful for topics like LCM, HCF, and divisibility rules. Mastering these will boost your speed in math competitions and board exams.
Classroom Tip
An easy way to remember the factors of 50 is notice that all numbers that both start and end divisibly, like 1 and 50, 2 and 25, 5 and 10, always come in pairs. Vedantu’s teachers use factor trees or pairs tables like above to help students see these patterns visually.
We explored factors of 50—from the basic definition, how to calculate, prime factorization, speed tricks, examples, and their relationship to other math concepts. For more practice and to get your questions answered, try Vedantu’s online maths sessions, which make building confidence in topics like these simple and fun!
Related pages for deeper learning:
Factors of 100 |
Factors of 60 |
Prime Factors |
Factors of a Number |
Difference Between Factors and Multiples
FAQs on Factors of 50: How to Find, List, and Understand Them
1. What are the factors of 50?
The factors of 50 are the numbers that divide 50 without leaving a remainder. These are 1, 2, 5, 10, 25, and 50. They represent all the numbers that can be multiplied together to equal 50.
2. What are the prime factors of 50?
The prime factors of 50 are the prime numbers that multiply to give 50. These are 2 and 5 (since 50 = 2 × 5 × 5 or 2 × 52). Prime numbers are only divisible by 1 and themselves.
3. How many factors does 50 have?
The number 50 has a total of six (6) factors: 1, 2, 5, 10, 25, and 50.
4. What is the prime factorization of 50?
The prime factorization of 50 is 2 × 5 × 5, or 2 × 52. This expresses 50 as a product of only prime numbers.
5. What are the factor pairs of 50?
The factor pairs of 50 are pairs of numbers that multiply to 50. These include (1, 50), (2, 25), and (5, 10). Note that (10, 5), (25, 2) and (50,1) are also valid pairs.
6. Is 8 a factor of 50?
No, 8 is not a factor of 50 because 50 divided by 8 leaves a remainder.
7. Is 20 a factor of 50?
No, 20 is not a factor of 50. 50 divided by 20 results in a remainder.
8. What are the common factors of 50 and 100?
The common factors of 50 and 100 are the numbers that divide both 50 and 100 without leaving a remainder. These are 1, 2, 5, 10, and 25.
9. Explain how to find all factors of a number.
To find all factors of a number, systematically check each integer from 1 up to half the number. If the number divides evenly, it's a factor. For example, for 50, check 1, 2, 3, 4... up to 25. You'll find 1, 2, 5, 10, 25, and 50 are all factors.
10. What is a factor tree, and how do I create one for 50?
A factor tree is a visual way to find the prime factorization of a number. For 50:
- Start with 50.
- Find two factors (e.g., 2 and 25).
- If a factor is not prime, continue breaking it down (25 = 5 × 5).
- Stop when all branches end in prime numbers (2, 5, and 5).
11. What is the difference between factors and multiples?
Factors divide a number evenly, while multiples are the result of multiplying a number by other integers. For example, the factors of 50 are 1, 2, 5, 10, 25, and 50. The multiples of 50 are 50, 100, 150, and so on.
12. How can I use prime factorization to find the greatest common factor (GCF) or least common multiple (LCM)?
Prime factorization helps find the GCF and LCM efficiently. Find the prime factorization of each number. The GCF is the product of the common prime factors raised to their lowest power. The LCM is the product of all prime factors raised to their highest power. For example, to find the GCF and LCM of 50 (2 x 52) and 100 (22 x 52), the GCF is 2 x 52 = 50 and the LCM is 22 x 52 = 100.
