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Chapter 10: Problem 614

Find the greatest common factor. $$5 n, 45$$

Short Answer

Expert verified
The greatest common factor is 5.

Step by step solution

01

List the Factors

List all the factors of each number. Factors of 5: 1, 5 Factors of 45: 1, 3, 5, 9, 15, 45
02

Identify Common Factors

Find the common factors from the lists. Common factors of 5 and 45: 1, 5
03

Find the Greatest Common Factor

Identify the greatest of the common factors. The greatest common factor of 5 and 45 is: 5

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Key Concepts

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

Factors
Factors are numbers that can evenly divide another number without leaving a remainder. For example, the factors of the number 10 are 1, 2, 5, and 10.
Each of these numbers can divide 10 without any leftovers.
To find the factors, you generally start with 1 and the number in question and try all the numbers in between.
Let's take a closer look at the factors of 5 and 45, as in the original exercise:
  • Factors of 5: 1 and 5
  • Factors of 45: 1, 3, 5, 9, 15, and 45
Common Factors
Common factors are factors that two or more numbers share.
From our original exercise, let's look at the common factors for the numbers 5 and 45.
First, as mentioned before, we list the factors:
  • Factors of 5: 1, 5
  • Factors of 45: 1, 3, 5, 9, 15, 45
The numbers 1 and 5 appear in both lists, so they are common factors.
Being aware of the common factors is very useful, particularly when simplifying fractions or finding the greatest common factor.
Prealgebra
Prealgebra involves foundational math skills that prepare you for algebra.
Learning to find the greatest common factor ranks as one of the essential prealgebra skills.
Understanding and mastering this concept helps with more complex algebraic tasks later.
For instance, you learn to simplify fractions.
If we have fractions like \(\frac{5}{45} \), we can simplify them by finding the greatest common factor, which is 5.
Dividing both the numerator and the denominator by 5 simplifies the fraction to \(\frac{1}{9} \).
Such exercises build a strong mathematical foundation, essential for algebra and beyond.

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Most popular questions from this chapter

Multiply the binomials using various methods. $$(x-8)(x+9)$$

Simplify. $$\frac{x}{x^{5}}$$

Simplify. $$\frac{2^{8}}{2^{2}}$$

Simplify each expression. $$\left(-\frac{3}{4}\right)^{3}$$

Divide the monomials. $$72 p^{12} \div 8 p^{3}$$
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