Can you find any numbers that have only one number in their list of prime factors?

Yes, numbers that have only one prime factor in their list are called **prime powers**. These numbers are of the form \( p^k \), where:

- \( p \) is a prime number (e.g., 2, 3, 5, 7, etc.), and
- \( k \) is a positive integer greater than or equal to 1.

For example:

- \( 2^3 = 8 \) has only one prime factor, which is 2.
- \( 3^2 = 9 \) has only one prime factor, which is 3.
- \( 5^1 = 5 \) has only one prime factor, which is 5.

In each of these cases, the prime number is repeated multiple times as a factor (depending on \( k \)).

Would you like more detailed examples or an explanation of how prime powers work?

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Here are 5 related questions:
1. What is the prime factorization of a number like 36?
2. How do we determine if a number is a prime power?
3. Can a number with two or more different prime factors be considered a prime power?
4. What is the significance of prime numbers in number theory?
5. How do prime powers differ from composite numbers?

**Tip:** Any prime number itself is also considered a prime power where \( k = 1 \). For example, 5 is both a prime number and a prime power.

Explore the concept of prime powers in number theory, where numbers are expressed as a power of a single prime factor. Learn examples like 2^3 = 8 and 3^2 = 9, and understand how the formula p^k is applied in mathematics. Suitable for students in Grades 6-8.

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