/*! 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 2 Find the greatest common factor.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 2

Find the greatest common factor. $$2,6,10$$

Short Answer

Expert verified
The greatest common factor of 2,6,10 is 2.

Step by step solution

01

Prime factorization

First, perform the prime factorization of each number. The prime factors of 2 are just 2, of 6 are 2 and 3, and of 10 are 2 and 5.
02

Identify common factors

Identify the common factors in each set of prime factors. In this case, the only common prime factor to all three numbers (2,6,10) is 2.
03

Calculate GCF

Calculate the greatest common factor. Since there is only one common prime number, 2, then it is the greatest common factor. Therefore, GCF(2,6,10) = 2.

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.

Prime Factorization
Prime factorization is the process of breaking down a number into the prime numbers that multiply together to create it. To begin, you might wonder what prime numbers are. A prime number is greater than 1 and can only be divided by itself and 1.
For example, let's look at the numbers from the exercise: 2, 6, and 10. The prime factorization for these numbers would be:
  • 2: The only prime factor is 2 itself.
  • 6: The prime factors are 2 and 3, because 2 times 3 equals 6.
  • 10: The prime factors are 2 and 5, since 2 times 5 equals 10.
Understanding prime factorization helps in finding the greatest common factor because it breaks down each number into its basic building blocks.
Common Factors
After determining the prime factors of a set of numbers, the next task is to identify the common factors. Common factors are the numbers that appear in each list of prime factors.
For the numbers 2, 6, and 10, we found these prime factors:
  • 2: Prime factors are {2}
  • 6: Prime factors are {2, 3}
  • 10: Prime factors are {2, 5}
If you look at these lists, the only prime number that appears in all three sets is 2. This shows that 2 is the common factor.
Recognizing common factors is essential to calculate the greatest common factor, which simplifies solving problems involving fractions or simplifying ratios.
Mathematical Problem Solving
Understanding how to solve mathematical problems using concepts like prime factorization and common factors is crucial for finding solutions efficiently. This structured approach can be applied to many problems beyond just finding the greatest common factor.
The process of solving the given problem involved:
  • Step 1: Breaking down each number into prime factors.
  • Step 2: Identifying which of these factors are common across all numbers.
  • Step 3: Choosing the greatest of these common factors as the solution.
Developing a step-by-step method like this can help tackle other mathematical challenges and improves problem-solving skills by applying logical thinking. Additionally, understanding these basic mathematical concepts forms a foundation for tackling more complex algebraic problems in the future.

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

When we add \(5 x\) and \(7 x\), we combine like terms: \(5 x+7 x=12 x\). Explain how this is related to factoring out a common factor.

Fill in the blanks. A polynomial that cannot be factored over the rational numbers is said to be a _____ polynomial.

Find the prime factorization of each number. $$288$$

Factor. If the polynomial is prime, so indicate. $$25+2 u^{2}+3 u$$

Factor each polynomial completely. If a polynomial is prime, so indicate. $$x^{4}-81$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics 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.