/*! 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 72 Find the GCF. $$24,36,48$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 72

Find the GCF. $$24,36,48$$

Short Answer

Expert verified
The greatest common factor of 24, 36 and 48 is 24.

Step by step solution

01

Prime Factorization of Each Number

Find the prime factors of each number. For 24, it鈥檚 2x2x2x3. For 36, it鈥檚 2x2x3x3. For 48, it鈥檚 2x2x2x2x3.
02

Identify Common Factors

Common prime factors to all three numbers are 2x2x2x3.
03

Multiply Common Factors

Now, multiply the common factors to get the GCF. So, 2 x 2 x 2 x 3 equals 24.

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 a way of expressing a number by multiplying together its prime numbers 鈥� these are numbers that can only be divided by 1 and themselves without leaving a remainder. For instance, let's explore the prime factorization of numbers 24, 36, and 48.
  • 24: To find the prime factors, divide 24 by the smallest prime number, which is 2. You get 12, which can again be divided by 2 to get 6, and once more by 2 to reach 3, a prime number. Thus, the prime factorization is: \( 2 \times 2 \times 2 \times 3 \).
  • 36: Starting again at 2, divide to get 18, then 9, which cannot be divided by 2, moving to the next prime number: 3. Divide 9 by 3 to get 3, leading to \( 2 \times 2 \times 3 \times 3 \).
  • 48: Divide by 2 to get 24, then by 2 three more times until reaching 3. The prime factorization is \( 2 \times 2 \times 2 \times 2 \times 3 \).
Knowing the prime factors is the stepping stone to identifying common factors, crucial for calculating the GCF.
Common Factors
Common factors are the prime numbers that appear in the prime factorization of each number under examination. It's essential to determine which of these factors are shared among all numbers to eventually find the Greatest Common Factor (GCF). For the numbers 24, 36, and 48, let's pinpoint these shared factors:
  • 24 has prime factors: \( 2 \times 2 \times 2 \times 3 \).
  • 36 has prime factors: \( 2 \times 2 \times 3 \times 3 \).
  • 48 has prime factors: \( 2 \times 2 \times 2 \times 2 \times 3 \).
Upon inspection, each number has at least two 2's and one 3 in their factorization. Hence, the common prime factors are \( 2 \times 2 \times 3 \). Identifying these shared factors is critical as they serve as the building blocks for calculating the GCF.
Multiplication of Factors
After determining the common factors, we move to multiplying them to find the Greatest Common Factor (GCF). This step involves a straightforward multiplication of all identified common factors. For our numbers 24, 36, and 48, the common factors were discovered to be \( 2 \times 2 \times 3 \).

To obtain the GCF, multiply these numbers together:
  • First, multiply the 2's: \( 2 \times 2 = 4 \).
  • Then, multiply the result by 3: \( 4 \times 3 = 12 \).
Thus, the GCF of 24, 36, and 48 is 12. This number is the largest factor that divides all the given numbers with zero remainder.

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

Divide and round to the nearest hundredth. Then check by estimating the quotient. $$6.398 \div 5.5$$

Convert the decimal to a fraction. $$0.125$$

You have \(\$ 20\) to spend, and you make purchases for the following amounts: \(\$ 4.24, \$ 8.66,\) and \(\$ .54 .\) Which of the following expressions correctly represent the amount of money you have left? (i) \(20-4.24+8.66+0.54\) (ii) \((4.24+8.66+0.54)-20\) (iii) \(20-(4.24+8.66+0.54)\) (iv) \(20-4.24-8.66-0.54\)

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$\frac{7}{12}$$

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{10}{11} \quad 0.909$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

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.