/*! 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 5 Find the GCF for each list. See ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 5

Find the GCF for each list. See Examples I through 3. $$ 24,14,21 $$

Short Answer

Expert verified
The GCF is 7.

Step by step solution

01

List the Factors

List all the factors of each number. - For 24: The factors are 1, 2, 3, 4, 6, 8, 12, 24. - For 14: The factors are 1, 2, 7, 14. - For 21: The factors are 1, 3, 7, 21.
02

Identify Common Factors

From the factor lists in Step 1, identify the factors that are common across all the numbers. - The common factors of 24, 14, and 21 are 1 and 7.
03

Determine the Greatest Common Factor

Out of the common factors identified in Step 2, find the greatest one. - The greatest common factor (GCF) of 24, 14, and 21 is 7.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Factors
Factors are numbers that divide another number without a remainder. In simpler terms, when you multiply two whole numbers together, each of them is a factor of the given product. For example, taking the number 24: when you multiply 2 by 12, or 3 by 8, or even 4 by 6, you achieve the product, 24. Thus, both numbers in each of these multiply instances are factors of 24. Here are additional points to remember about factors:
  • The number 1 is a universal factor; it is a factor of every number.
  • Every number is a factor of itself; hence, 24 is also a factor of 24.
  • When listing factors, always start with 1 and the number itself, then identify the other pairs.
Identifying factors is a basic step in many math operations and crucial for determining the greatest common factor.
Exploring Common Factors
Common factors are the factors that two or more numbers share. When finding common factors, one must first list out the factors of each number individually. Then, compare those lists to spot numbers that appear in every list. These shared numbers are the common factors. For example, with numbers 24, 14, and 21:
  • Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
  • Factors of 14 are: 1, 2, 7, 14
  • Factors of 21 are: 1, 3, 7, 21
Looking through these lists, we find that 1 and 7 are present in all three. So, the common factors are 1 and 7. Identifying these shared figures helps in calculating the greatest factor that numbers collectively possess.
Solving the Problem of Greatest Common Factor
Problem solving involving the greatest common factor (GCF) involves several logical steps. Based on the example of numbers 24, 14, and 21, the GCF is found by following these outlined steps. First, after listing the individual factors, we identify all the common factors. Check the commonality across all lists, which for our case yields 1 and 7. The GCF is the largest of these common factors, which is 7 in this instance. When solving such problems, always remember these helpful tips:
  • Carefully verify every factor list.
  • Cross-reference for the highest shared factor.
  • Understand that the GCF can be useful for simplifying fractions and solving ratio problems.
Practicing this structured approach ensures accuracy and enhances problem-solving skills in finding the GCF efficiently.

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

Solve each equation. See Examples I and 2. $$ (x+1.7)(x+2.3)=0 $$

Factor out the GCF from each polynomial. See Examples 4 through 10. $$ 30 x-15 $$

Solve each equation. See Examples I and 2. $$ (2 x+3)(4 x-5)=0 $$

Factor each trinomial completely. See Examples I through II and Section 6.2. \(5 m^{5}+26 m^{3} h^{2}+5 m h^{4}\)

Write a polynomial that factors as \((x-3)(x+8)\).
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.