Problem 6 Find the greatest common factor.... [FREE SOLUTION]

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Chapter 7: Problem 6

Find the greatest common factor. \(5 b, 30\)

Short Answer

Expert verified

The greatest common factor is 5.

Step by step solution

- Determine the Factors of Each Term

List all the factors of each term. Factors of 5b are: 1, 5, b, 5b.Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.

- Identify Common Factors

Look for common factors in the two lists. The common factors between 5b and 30 are: 1 and 5.

- Determine the Greatest Common Factor

The greatest factor common to both 5b and 30 is 5.

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Key Concepts

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

Factors

Understanding factors is the first step in finding the greatest common factor (GCF).
Factors are numbers you can multiply to get another number.
For example, if you have the number 30, you can find its factors by asking, 'What numbers can I multiply to get 30?' Some of the answers are 1, 2, 3, 5, 6, 10, 15, and 30.
These are all the factors of 30.
It鈥檚 like solving a puzzle by finding all the pieces that fit with 30.
Breaking down numbers by their factors is an essential skill in math.
It helps in simplifying fractions, solving equations, and more.
To find factors, take each number and figure out all the combinations of numbers that can multiply together to make it.

Common Factors

After you understand factors, the next step involves common factors.
Common factors are simply factors that are shared by two or more numbers.
Imagine you have two lists:

One list for the factors of 5b: 1, 5, b, 5b
Another list for the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

To find common factors, just look for numbers that appear in both lists.
In this case, the common factors are 1 and 5.
This is a crucial step because it identifies the numbers that are involved with both original numbers.
Spotting common factors is an important skill in various math problems.

Greatest Common Factor

The greatest common factor (GCF) is the biggest number that is a common factor for the given terms.
Using our example of 5b and 30:

The factors of 5b are 1, 5, b, 5b
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The common factors between them are 1 and 5

Out of these common factors, 5 is the greatest.
So, the GCF of 5b and 30 is 5.
Why is finding the GCF useful? In math, it simplifies lots of problems.
For example, when you are working with fractions, the GCF helps you simplify them by reducing both the numerator and the denominator in the same way.
Mastering GCF assists in many areas of mathematics, from basic arithmetic to advanced algebra.

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91影视

Find the greatest common factor. \(5 b, 30\)

Short Answer

Step by step solution

- Determine the Factors of Each Term

- Identify Common Factors

- Determine the Greatest Common Factor

Key Concepts

Factors

Common Factors

Greatest Common Factor

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