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Chapter 7: Problem 4

Find the greatest common factor. 150,275

Short Answer

Expert verified
25

Step by step solution

01

- List the Prime Factors of Each Number

First, list out the prime factors of each number. The prime factors of 150 are: 150 = 2 脳 3 脳 5 脳 5 The prime factors of 275 are: 275 = 5 脳 5 脳 11
02

- Identify Common Prime Factors

Next, identify the common prime factors between the two sets of factors. Both 150 and 275 have the common prime factors: 5 and 5.
03

- Multiply the Common Prime Factors

Multiply the common prime factors together to find the greatest common factor (GCF). GCF = 5 脳 5 = 25

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Key Concepts

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

Prime Factorization
To find the greatest common factor (GCF), the first step is prime factorization. This means breaking down each number into its prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. For number 150, the prime factors would be: 150 = 2 脳 3 脳 5 脳 5. And for 275, the prime factors are: 275 = 5 脳 5 脳 11. Prime factorization helps us see the building blocks of each number clearly, making it easier to find common factors.
Common Factors
After listing out the prime factors, the next step is identifying common factors. Common factors are the prime numbers that appear in both lists. For the numbers 150 and 275, the common prime factors are 5 and 5. Highlighting common factors helps us see what these numbers share, which is crucial for finding the GCF. The more organized we are in listing these factors, the easier it will be to spot the common ones.
Multiplication of Factors
Once the common prime factors are identified, the final step is multiplying these common factors together. In our example, the common prime factors for both 150 and 275 are 5 and 5. Therefore, to find the GCF, we multiply these together: GCF = 5 脳 5 = 25. This multiplication step consolidates the shared factors into the greatest common factor, giving us the answer. Understanding the multiplication of factors is vital to completing the process and arriving at the correct GCF.

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