Log out Go to App
Go to App

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

$$ \text { If } 0

If \(a, b\), and \(c\) are distinct prime numbers, how many factors does abc have?

If \(x=\sqrt{25}\), which of the following is true? $$ \begin{aligned} & \text { C } x=5 \\ & x=-5 \\ & x=\pm 5 \\ & \text { I don't know. } \\ & \end{aligned} $$

In 40 seconds, a mountain biker travels 230 feet. What is her speed in miles per hour? (Note: 1 mile \(=5280\) feet) $$ \begin{array}{r} \frac{230 \times 60 \times 60}{40 \times 5280} \\ \frac{230 \times 5280}{40 \times 60 \times 60} \\ \frac{40 \times 60 \times 60}{230 \times 5280} \\ \text { I don't know. } \end{array} $$

If \(0x^2 $$ \(x
See all solutions

Recommended explanations on English Textbooks

Language Acquisition

Read Explanation

International English

Read Explanation

Semiotics

Read Explanation

Global English

Read Explanation

Argumentative Essay

Read Explanation

English Language Study

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free