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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 correct answer is a. Quantity A is greater.

Step by step solution

01

Finding the Greatest Odd Factor of 78

To find the greatest odd factor of 78, we can start by listing all the factors of 78: 1, 2, 3, 6, 13, 26, 39, and 78. Among these, the odd factors are 1, 3, 13, and 39. Therefore, the greatest odd factor of 78 is 39.
02

Finding the Greatest Prime Factor of 78

To find the greatest prime factor of 78, we again look at the list of factors. The prime factors of 78 are 2, 3, and 13. Hence, the greatest prime factor of 78 is 13.
03

Comparing Quantities A and B

After finding that the greatest odd factor of 78 (Quantity A) is 39 and the greatest prime factor of 78 (Quantity B) is 13, we can determine that Quantity A is larger than Quantity B.

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