Name:    Factors and Prime Numbers

True/False
Indicate whether the statement is true or false.

1.

Indicate whether if the statement is true or false:
All prime numbers are rational

2.

Indicate whether if the statement is true or false:
All imaginary numbers are irrational

3.

Indicate whether if the statement is true or false.
All fractions are rational numbers.

4.

Indicate whether if the statement is true or false:

All perfect squares have an odd number of distince prime factors.

Multiple Response
Identify one or more choices that best complete the statement or answer the question.

5.

Indicate which of the following are irrational numbers:
 a. e. b. f. c. g. d. h.

6.

Indicate which of the following are irrational numbers:
 a. d. b. e. c.

Multiple Choice
Identify the choice that best completes the statement or answers the question.

7.

Suppose , where “a”, “b”, and “c’ are prime numbers and “n”, “m” and “p” are whole numbers.  Which of the following expressions is equal to the number of factors that “N” has?
 a. c. b. d.

8.

Suppose , how many factors does “N” have?
 a. c. b. d.

9.

Suppose the prime factorization of “N” is , where “m”, “n” and “p” are prime factors, and “a”, “b”, and “c” are whole numbers.  Which of the expressions below gives the sum of all the factors?
 a. b. c. d.

10.

What is the sum of all the factors of
 a. 11,284 c. 2,916,000 b. 97,200 d. 349,804

Numeric Response

11.

Evaluate without a calculator.

12.

Evaluate without a calculator.

13.

Esimate

14.

, what is the value of a+b?

15.

, what is the value of a+b?

16.

k=, what is the lowest value of “N” so that “k” is an integer.  Note, “N” must be a positive integer

17.

What is the 1000th digit in the decimal expansion of ?

18.

What is the smallest number that has 20 factors?

19.

What is the sum of all integers less than 100 with exactly 12 positive factors?

20.

How many factors does have?