1.a. Find the prime factorization of 520 using any method.

b. Determine the number of positive divisors 520 has by using the exponents of its prime factorization.

c. Use the square root method to determine if the number 253 is prime or composite.

2.a. What is the GCF any of two relatively prime numbers?

b. What is the LCM of any two relatively prime numbers?

3.For each of the following, explain (using the divisibility rules) why 214810 is (or is not) divisible by:

a)2

b)3

c)4

d)5

e)6

f)8

g)9

h)10

i)11 (you only need to show how to use the divisibility test, you do not need to explain it):

4.Find the GCF (108, 72) using any method we used in class and show your method.

5.Find the LCM (48, 56) using any method we used in class and show your method.

6.Find the LCM (8, 12, 24) using the division by primes method (also called the ladder method or the cake method).

7.Pencils come in packages of 18; erasers that fit on the top of these pencils come in packages of 24. What is the smallest number of pencils and erasers that you can buy so that each pencil will be matched with an eraser? How many packages of pencils will you need and how many packages of erasers? (You must buy whole packages - no partials!)

8.Name the four different ways we use fractions.

a.

b.

c.

d.

9.Show two different methods for determining ifandare equivalent fractions.