Download Name Date Objective: 6M.1.1.2 Use prime factorization to • express

Name _______________________________________ Date _______________
•
Objective: 6M.1.1.2
Use prime factorization to
• express a whole number as a product of its prime factors and
determine the greatest common factor and least common multiple of two
whole numbers.
Directions: Read each problem. Choose the correct answer.
1. What is the least common multiple (LCM) of 30 and 45?
A. 90
B. 45
C. 15
D. 1,350
2. What is the prime factorization for 12?
A. 3 × 42
B. 2 × 32
C. 3 × 4
D. 22 × 3
3. What is the prime factorization for 150?
A. 35 × 52
B. 2 × 32 × 5
C. 2 × 3 × 52
D. 6 × 52
4. What is the greatest common factor (GCF) of 36 and 120?
A. 4
B. 12
C. 6
D. 60
5. What is the prime factorization for 900?
A. 2 × 32 × 52
B. 25 × 52 × 9
C. 22 × 52 × 9
D. 22 × 32 × 52
6M.1.1.2 Answers:
1. A
Find the prime factorization of each number.
1
1
2
1
30 = 2 × 3 × 5 = 2 × 3 × 5
45 = 3 × 3 × 5 = 3 × 5
1
To find the least common multiple, multiply together the largest power of each prime shown.
1
The largest power of 2 shown is 2 .
2
The largest power of 3 shown is 3 .
1
The largest power of 5 shown is 5 .
So, the least common multiple is:
1
2
1
2. 2 × 3 × 5 = 90
2.
D
One way to find the prime factorization of a number is to repeatedly divide by prime
numbers until a prime number is left.
12 ÷ 2 = 6
6÷2=3
2
Thus, 12 = 2 × 2 × 3 = 2 × 3.
3.
C
One way to find the prime factorization of a number is to repeatedly divide by prime
numbers until a prime number is left.
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
2
Thus, 150 = 2 × 3 × 5 × 5 = 2 × 3 × 5 .
4.
B
Find the prime factorization of each number.
2
36 = 2 × 2 × 3 × 3 = 2 × 3
2
3
1
120 = 2 × 2 × 2 × 3 × 5 = 2 × 3 × 5
1
To find the greatest common factor, multiply together the highest power of each prime
that both numbers share.
The highest power of 2 that both 36 and 120 have is 2.
The highest power of 3 that both 36 and 120 have is 1.
So, the GCF is:
2
1
2 × 3 = 12.
5.
D
One way to find the prime factorization of a number is to repeatedly divide by prime
numbers until a prime number is left.
900 ÷ 2 = 450
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
2
2
2
Thus, 900 = 2 × 2 × 3 × 3 × 5 × 5 = 2 × 3 × 5 .