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Chapter 14: Problem 7

Quantity \(\mathbf{A}\) The greatest odd factor of 78 Quantity \(\mathbf{B}\) The greatest prime factor of 78 a. Quantity A is greater. b. Quantity B is greater c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
The answer is a. Quantity A (the greatest odd factor of 78) is greater.

Step by step solution

01

Identifying the Factors

The first step is to identify all the factors of 78. The factors are \(1, 2, 3, 6, 13, 26, 39, 78\)
02

Identify Odd Factors

Next, identify the odd factors. These are \(1, 3, 13, 39\). The greatest odd factor is \(39\), which becomes Quantity A.
03

Identify Prime Factors

Now, identify the prime factors. These are \(2, 3, 13\). The greatest prime factor is \(13\), which becomes Quantity B.
04

Compare Quantities A and B

Finally, compare Quantity A, which is \(39\), and Quantity B, which is \(13\). It is clear that Quantity A is greater

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