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Chapter 10: Problem 12

Determine the greatest common factor. 15 and 20

Short Answer

Expert verified
The greatest common factor of 15 and 20 is 5.

Step by step solution

01

- List the Factors of Each Number

First, determine all the factors of each number. Factors of 15 are: 1, 3, 5, and 15. Factors of 20 are: 1, 2, 4, 5, 10, and 20.
02

- Identify the Common Factors

Next, find the factors that appear in both lists. Common factors of 15 and 20 are: 1 and 5.
03

- Determine the Greatest Common Factor

Finally, out of the common factors, select the largest one. The greatest common factor of 15 and 20 is 5.

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Key Concepts

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

Factors of Numbers
Factors are numbers that can be multiplied together to get another number. For example, the factors of 6 are 1, 2, 3, and 6 because:
1 * 6 = 6
2 * 3 = 6
Every number has at least two factors: 1 and itself. To find all the factors of a number, you can start by checking if 1 and the number itself multiply to the given number. Then, continue with increasing numbers to see if their multiplication results match the original number.
Common Factors
Common factors of two or more numbers are the factors that those numbers have in common. To find common factors, follow these steps:
  • List the factors of each number.
  • Compare the lists to identify any numbers that are the same in both lists.
  • These shared numbers are the common factors.
For example, for the numbers 15 and 20:
* Factors of 15: 1, 3, 5, 15
* Factors of 20: 1, 2, 4, 5, 10, 20
The common factors are the numbers that appear in both lists: 1 and 5.
Step by Step Solution to Find the Greatest Common Factor
Finding the greatest common factor (GCF) involves a few straightforward steps. Let's break it down using the example of finding the GCF of 15 and 20.
  • Step 1: List the factors of each number. Factors of 15 are 1, 3, 5, and 15. Factors of 20 are 1, 2, 4, 5, 10, and 20.
  • Step 2: Identify the common factors. Look for numbers that are in both lists of factors. Here, both 15 and 20 share the factors 1 and 5.
  • Step 3: Determine the greatest common factor. Out of the common factors, the greatest (largest) one is 5. Therefore, the GCF of 15 and 20 is 5.
By following these steps, you can find the GCF for any pair of numbers, making it easier to simplify fractions or solve other math problems.

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Most popular questions from this chapter

Subtract \(\left(9 x^{2}+16 x-4\right)\) from \(\left(2 x^{2}-4 x-9\right)\)

Simplify the expression. $$\left(2 p^{2}\right)^{3}(p q)^{2}$$

The cost (in dollars) for a cab ride is given by the polynomial \(2+1.25 x+\) \(0.25 y .\) In this context, \(x\) is the number of miles driven and \(y\) is the time in minutes for the ride. a. Evaluate the polynomial for \(x=10\) and \(y=20 .\) Interpret the answer in the context of this problem. b. Evaluate the polynomial for \(x=22\) and \(y=40 .\) Interpret the answer in the context of this problem.

Simplify. Write the answers with positive exponents only. $$\left(x^{2}\right)^{4}\left(x^{5}\right)^{-2}$$

Simplify. Write the answers with positive exponents only. $$\frac{2^{3}}{2^{-2}}$$
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