Directions: Follow the instructions for each problem set below.
Factor each number below. Then use exponents to write each prime factorization.
1) 36
2) 51
3) 32
4) 75
Write the composite number for each prime factorization. You may wish to use a calculator.
5) 22
x 3 x 52
6) 2x32x7
7) 33
x 5
8) 2 x 53
Mixed Applications
Solve the following problems.
9) Find all the numbers with prime factors 2, 3, and 7 that equal less than 200.
10) If a number is divisible by 4 and 7, the number must have at least six factors. What are they?
NUMBER SENSE
Explain the pattern in the following problem.
11) What number comes next? 9, 25, 49, 81, 121, ______
Greatest Common Factor
List the factors of each number. Then find the GCF.
12) 18, 27
13) 28, 35
14) 12, 15
Use prime factorization to find the GCF.
15) 15, 35
16) 24, 36
17) 21, 45
Mixed Applications
Use the information given to solve the following problems.
Forest City has ordered 36 maple trees and 54 dogwood trees to be planted in groups in a city park. Each group will have the same number of maple trees and dogwood trees.
18) Can the trees be planted in:
a. 6 groups?
b. 8 groups?
c. 9 groups?
19) What is the greatest number of groups that can be planted? How many trees of one kind can be in one group?