There are two prime number factors of 45.
Understanding Factors and Prime Numbers
Before we dive into the factors of 45, let's clarify some key terms:
- Factors: Factors are numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime Number: A prime number is a whole number greater than 1 that has only two factors: 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.
Finding the Factors of 45
According to the reference, the factors of 45 are 1, 3, 5, 9, 15, and 45. Let's examine these to see which ones are prime.
Identifying Prime Factors of 45
The reference states that the prime factorization of 45 is 1 x 3 x 3 x 5, and thus the prime factors are 3 and 5. Here's a breakdown:
- 1: Not a prime number, as prime numbers must have exactly two distinct factors, and 1 only has one factor.
- 3: A prime number, as it is only divisible by 1 and itself.
- 5: A prime number, as it is only divisible by 1 and itself.
- 9: Not a prime number, because it is divisible by 1, 3, and 9.
- 15: Not a prime number, because it is divisible by 1, 3, 5, and 15.
- 45: Not a prime number, because it is divisible by 1, 3, 5, 9, 15 and 45.
Therefore, the prime factors of 45 are 3 and 5. There are two prime factors of 45.
| Factor | Prime? |
|---|---|
| 1 | No |
| 3 | Yes |
| 5 | Yes |
| 9 | No |
| 15 | No |
| 45 | No |
Conclusion
In conclusion, out of all the factors of 45 (1, 3, 5, 9, 15, and 45), only two are prime numbers: 3 and 5.
