Download Challenge 3-1

Name
LESSON
Date
Class
Challenge
3-1 A Different Point of View
Create two more factor trees with different factors for
each number.
1.
225
25
5
225
225
9
5
3
3
Prime factorization of 225:
2.
504
3
504
168
8
4
2
504
21
2
7
3
2
Prime factorization of 504:
3. In 1742, Christian Goldbach wrote his now famous Goldbach’s
Conjecture, which states that every even number greater than 2
can be represented as the sum of 2 primes. Although this
conjecture is still an open question, it can be supported. Choose
3 even numbers greater than 2 to help support Goldbach’s
Conjecture.
4. Goldbach also made a conjecture that every odd number is the
sum of 3 primes. Choose 3 odd numbers to support this conjecture.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
9
Holt Mathematics
Problem Solving
3-1 Prime Factorization
Challenge
3-1 A Different Point of View
LESSON
LESSON
Write the correct answer.
Create two more factor trees with different factors for
each number. Possible answers are given.
1.
225
25
5
225
15
9
5
3
15
5
45
3 5 3 5
3
1. The width of a swimming pool (in
feet) is a prime number greater than
10. The width and length of the pool
are factors of 408. What are the
dimensions of the pool?
225
5 9
2. The area of the dining room at
Thomas Jefferson’s home in
Monticello is about 342 square feet. If
the approximate length of one side is
a prime number less than 25, what
are the approximate dimensions of
the room?
3 3
Prime factorization of 225:
2.
32 • 52
504
3
504
8
2
2
168
4
17 ft by 24 ft
3
21
2
7
504
252
84
2
12 7
3
4
2
2
Prime factorization of 504:
3
63
8
4 7
2
9
2 3
3
3
2
2
2 •3 •7
Possible answer: 12 7 5; 32 19 13; 44 13 31
4. Goldbach also made a conjecture that every odd number is the
sum of 3 primes. Choose 3 odd numbers to support this conjecture.
Possible answer: 13 3 5 5; 15 5 5 5; 33 23 5 5
9
Holt Mathematics
5 groups of 50; 2 groups of 125;
29 pages per day for
10 groups of 25
15 days
5. There are 228 seventh graders. Each
seventh-grade homeroom starts the
year with the same number of
students and has at least 15
students. What is the least number of
rooms that are needed?
A 17
B 19
C 12
D 21
6. Solve this riddle: I am a number
whose prime factors are all the prime
numbers between 6 and 15. No factor
is repeated. What number am I?
F 9,009
G 91
H 1,001
J 6,006
7. What is the prime factorization of
1,485?
A 3 • 3 • 3 • 5 • 11
B 3 • 3 • 5 • 5 • 11
C 3 • 5 • 9 • 11
D 5 • 11 • 27
8. Solve this riddle: I am a prime factor
of 39 and 65. What number am I?
F 3
G5
H 11
J 13
Reading Strategies
3-1 Compare and Contrast
Puzzles, Twisters & Teasers
3-1 Can You Find All the Words?
Solve the word search, then find the word from the list that best
completes the riddle.
Whole Numbers
Prime Number
• Has only two factors:
itself and 1.
Examples
2
2•12
5
1•55
step
unique
composite
factor
factorization
exponent
tree
prime
diagram
Hajratwala
Composite Number
• Has more than two factors.
Examples
6
1•66
2•36
9
1•99
3•39
P R I M E F U N I Q U E P
C
T
E
F
A
C
T
O
A composite number can be written as the product of prime
numbers. This is called prime factorization.
A factor tree helps you find all prime factors of a number.
9 and 8 are not prime numbers.
Continue to factor.
2 is a prime number. Circle 2.
4 is not a prime number.
Continue to factor.
8
3 • 3 4 • 2
2
2
W
Y
R
A
S
G
N
W
E
P
T
C
Z
B
M
E
S
L
Y
T
R
E
E
R
A
M
U
O
A
X
A
T
H
A
J
R
A
T
W
A
D
S
C
I
Q
D
N
T
C
X
F
Z
W
S
J
H
B
D
T
A
R
A
I
N
N
S
S
T
E
P
L
B
U
R
Y
I
I
B
K
V
O
W
C
O
M
P
O
S
F
K
B
N
F
M
C
I
R Y U I O L C V B N M I L
A S E D I A G R A M F T W
72
•
Holt Mathematics
LESSON
Whole numbers are either prime numbers or composite numbers.
Compare the differences between them.
9
10
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
LESSON
3 is a prime number.
Circle both 3’s.
2 is a prime number.
Circle both 2’s.
4. You want to read a mystery that has
435 pages. If you read the same
number of pages per day and the
number is a prime number greater
than 20, how many pages per day
will you read?
Choose the letter of the best answer.
3. In 1742, Christian Goldbach wrote his now famous Goldbach’s
Conjecture, which states that every even number greater than 2
can be represented as the sum of 2 primes. Although this
conjecture is still an open question, it can be supported. Choose
3 even numbers greater than 2 to help support Goldbach’s
Conjecture.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
19 ft by 18 ft
3. A university has a lounge that can be
converted into a meeting hall for 250
people. If the hall is filled and
everyone is in equal groups, what are
the different ways the people can be
grouped so that there are no more
than 10 groups?
W S C E X P O N E N T E J
What was the mathematician’s favorite food?
P
The prime factorization of 72 is 3 • 3 • 2 • 2 • 2, or 32 • 23.
R
I
M
E
rib
Answer each question.
1. What is the difference between a prime number and a
composite number?
A prime number has only two factors, itself and 1. A composite number
has more than two factors.
2. Find the prime factorization of 48.
2 • 2 • 2 • 2 • 3, or 24 • 3
3. Find the prime factorization of 56.
2 • 2 • 2 • 7, or 23 • 7
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
11
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
64
12
Holt Mathematics
Holt Mathematics