Download Prime Factorization

Number Theory
and Systems
Teacher Key
Prime Factorization
Sort the numbers in the bank as either prime numbers or composite numbers.
A. Prime Numbers
B. Composite Numbers
2
6
5
9
7
10
17
21
23
35
Bank
35
6
5
7
21
10
17
23
9
2
Draw factor trees for the following numbers
C.
225
5
D.
400
45
5
5
5
5
4
9
3
3
E. The prime factorization of 225 is
3x3x5x5
100
2
2
2
50
2
2
2
2
2
2
2
2
25
5
5
F. The prime factorization of 400 is
.
2x2x2x2x5x5
.
G. How can you check your answer?
The product of the prime factors equals the original number.
© 2003 CompassLearning, Inc.
Activity 67114
Number Theory
and Systems
Teacher Key
Prime Factorization
Complete each factor tree.
H.
I.
80
40
20
4
5
2
2
2
2
2
2
5
2
8
16
4
4
2
2
128
2 2
2
4
2
2
2
2
2
Find all the possible solutions.
J. A number is less than 50. The number is prime. The sum of the digits is 5. What is the
number?
The number is 23 or 41.
K. A number is less than 30. The number is composite. The sum of digits is 7. The
product of the digits is 10. What is the number?
The number is 25.
L. A number is less than 100. The number is composite. The sum of the digits is 15.
What is the number?
The number is 69, 96, 78, or 87.
© 2003 CompassLearning, Inc.
Activity 67114
Number Theory
and Systems
Teacher Key
Connections
Think About It
Can you find the greatest prime number? Why or why not?
SAMPLE RESPONSE: No, you cannot find the greatest prime number. Since
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numbers are infinite, so are prime numbers. Therefore, there is always a prime
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number greater than the one you just found. It is a never-ending cycle.
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The Sieve of Eratosthenes
In ancient Greece, a mathematician named Eratosthenes formulated a technique for
finding prime numbers. Follow his technique for numbers less than 100 and discover 25
prime numbers. The numbers 1 through 100 are listed on the following page for you.
Instructions
! Cross out 1, since it is not considered a prime number.
! Draw a circle around the first prime number, 2. Then, cross out every multiple of 2.
! Draw a circle around the next prime number, 3. Then, cross out every multiple of 3.
You may skip any numbers already crossed out.
! Draw a circle around the next number not crossed out, 5. Then, cross out every
multiple of 5. Again, you may skip any numbers already crossed out.
! Continue this process until all the numbers are either circled or crossed. The circled
numbers are the prime numbers less than 100.
Did you find 25 prime numbers? If not, go back and check your method.
© 2003 CompassLearning, Inc.
Activity 67114
Number Theory
and Systems
Teacher Key
Connections
© 2003 CompassLearning, Inc.
Activity 67114