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

Short Answer

Expert verified
The product of three distinct prime numbers, \(abc\), has 8 factors.

Step by step solution

01

Identify the Number of Factors for Prime Numbers

Every prime number has only two factors, namely 1 and the prime number itself.
02

Multiply the Prime Numbers

Multiplying the prime numbers \(a, b, c\) produces a composite number. This composite number has \(a, b, c\), and 1 as factors.
03

Consider the Interactions Between Two Numbers

Multiplying any two of the distinct prime numbers will produce new, distinct factors. These are \(ab, ac, bc\).
04

Determine the Total Number of Factors

Adding all distinct factors found earlier, which are \(1, a, b, c, ab, ac, bc, abc\), we find that \(abc\) has 8 factors.

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.

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

Study anywhere. Anytime. Across all devices.

Sign-up for free