/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 Find the greatest common divisor... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 20

Find the greatest common divisor \(\\{15,28\\}\).

Short Answer

Expert verified
The Greatest Common Divisor (GCD) of 15 and 28 is 1, as there are no common prime factors between the two numbers. \(GCD(15,28) = 1\).

Step by step solution

01

Prime Factorization

First, we will find the prime factors of each number. Prime factors are the prime numbers that you multiply together to get the original number. For 15: 15 = 5 脳 3 (5 and 3 are prime numbers) For 28: 28 = 7 脳 2 脳 2 (7 and 2 are prime numbers) So, the prime factorization of 15 is 3 脳 5 and that of 28 is 2 脳 2 脳 7.
02

Identifying Common Prime Factors

Now we will identify the prime factors that both numbers have in common. From the prime factorizations, we can see that there are no common prime factors between 15 and 28. So, there is no prime number that can divide both numbers at the same time, leaving no remainders.
03

Calculating the GCD

Since there are no common prime factors between the two numbers, the greatest common divisor is 1. In other words, 15 and 28 are relatively prime, and the largest positive integer that divides both numbers without leaving a remainder is 1. The Greatest Common Divisor (GCD) of 15 and 28 is 1.

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 91影视!

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

Find the greatest common divisor of 24 and 40 . Also, find the least common multiple of 24 and 40 .

Find the Least Common Multiple, LCM, of 12 , \(18,21,25\) and 35 .

Find the least common multiple ( \(1 \mathrm{~cm}\) ) of 15 and 18 .

Find the Least Common Multiple, LCM, of 26,39 , and 66

Find the greatest common divisor and the least common multiple of 16 and 12 .
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

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.