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Chapter 7: Problem 2

Even integer q is the product of two distinct prime numbers. What can you say about the factors of q?

Short Answer

Expert verified
The factors of q will always be 1, 2, the distinct odd prime number, and the even integer q itself.

Step by step solution

01

Identify the even prime number

The only even prime number is 2. Therefore, for the product of two prime numbers to be even, one of the prime numbers must be 2.
02

Identify the other prime number

Since the two prime numbers are distinct, the other prime number must be an odd prime number. Let this odd prime number be represented by \( p \). The possible values for \( p \) could be any prime number other than 2.
03

Determine the product

The product of the two prime numbers, \( q = 2p \). The factors of \( q \) will therefore be 1, 2, \( p \) and \( 2p \).
04

Conclusion

Therefore, the factors of \( q \) when \( q \) is the product of two distinct prime numbers will always be 1, 2, the odd prime number, and the even integer \( q \) itself.

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