Question
upstudy study bank question image url

Find the greatest common factor. \[ 8 h^{2}, 2 h^{3} \]

Ask by Byrd Ellis. in the United States
Mar 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The greatest common factor of \(8h^2\) and \(2h^3\) is \(2h^2\).

Solution

To find the greatest common factor (GCF) of the expressions \(8h^2\) and \(2h^3\), we can follow these steps: 1. **Identify the coefficients**: The coefficients are 8 and 2. 2. **Identify the variable parts**: The variable parts are \(h^2\) and \(h^3\). ### Step 1: Find the GCF of the coefficients The GCF of 8 and 2 can be calculated as follows: - The factors of 8 are: \(1, 2, 4, 8\) - The factors of 2 are: \(1, 2\) The greatest common factor of 8 and 2 is **2**. ### Step 2: Find the GCF of the variable parts For the variable parts \(h^2\) and \(h^3\): - The GCF is determined by taking the lowest power of \(h\) present in both terms, which is \(h^2\). ### Step 3: Combine the GCFs Now, we combine the GCF of the coefficients and the GCF of the variable parts: \[ \text{GCF} = 2h^2 \] Thus, the greatest common factor of \(8h^2\) and \(2h^3\) is \(\boxed{2h^2}\).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

To find the greatest common factor (GCF) of \(8 h^{2}\) and \(2 h^{3}\), we first look at the coefficients. The GCF of 8 and 2 is 2. Next, we consider the variable part; the GCF of \(h^{2}\) and \(h^{3}\) is \(h^{2}\) since we take the lowest power. Therefore, the GCF of \(8 h^{2}\) and \(2 h^{3}\) is: \[ 2 h^{2} \] Now you have the greatest common factor! Think of the GCF as the ultimate team player! Just like in a sports team where the best players complement each other, the GCF finds common ground between numbers and variables, bringing them together to simplify expressions or solve problems. It's all about teamwork making the dream work in math! Have you ever wondered how you might encounter GCF in real life? Imagine splitting a pizza! If you have two pizzas with 8 and 2 toppings respectively, the GCF helps you figure out how to share them evenly. GCF not only makes math easier, but it also comes in handy in everyday decisions!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy