Which of the following numbers has the most unique prime factors? Numbers: 15, 19, 27, and 31.

To determine which of the given numbers has the most unique prime factors, let's break down each number into its prime factors:

1. **15**: 
   - Prime factorization: \(15 = 3 \times 5\)
   - Unique prime factors: 2 (which are 3 and 5)

2. **19**: 
   - Prime factorization: \(19\) (19 is a prime number)
   - Unique prime factors: 1 (which is 19)

3. **27**: 
   - Prime factorization: \(27 = 3 \times 3 \times 3 = 3^3\)
   - Unique prime factors: 1 (which is 3)

4. **31**: 
   - Prime factorization: \(31\) (31 is a prime number)
   - Unique prime factors: 1 (which is 31)

Now, let's summarize the number of unique prime factors for each number:

- **15**: 2 unique prime factors
- **19**: 1 unique prime factor
- **27**: 1 unique prime factor
- **31**: 1 unique prime factor

**Conclusion**: The number **15** has the most unique prime factors, with a total of 2.

Would you like more details or have any questions?

Here are 8 related questions to explore further:
1. How do you determine the prime factors of a number?
2. What is the prime factorization of 60?
3. How would the prime factorization of 45 look?
4. What is the largest prime number under 50?
5. How many unique prime factors does 100 have?
6. Can two different numbers have the same set of prime factors?
7. What is the difference between a prime number and a composite number?
8. How would you find the prime factors of a large number efficiently?

**Tip:** Remember, a prime factor is a factor that is a prime number itself, and no prime number has more than one unique prime factor.

Discover which of the numbers 15, 19, 27, and 31 has the most unique prime factors. Explore their prime factorizations and learn how to determine unique prime factors efficiently. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation