Download 9-2 Prime Factorization

9-2 Prime Factorization
Determine whether each number is prime or composite.
26
26 = 1 26
26 = 2 13
The factors of 26 are 1, 2, 13, and 26. Since the number has more than two factors, it is a composite number.
19
19 = 1 19
The number 19 has only two factors, 1 and 19. So, 19 is a prime number.
35
35 = 1 35
35 = 5 7
The factors of 35 are 1, 5, 7, and 35. Since the number has more than two factors, it is a composite number.
MULTIPLE CHOICE There are 30 students going on a field trip to an art museum. What is the prime
factorization of 30?
2
A2 3 5
B2 3 5
C 32 5
2
D2 5
Choice B is correct.
Factor each monomial.
3
14a
2
9rs t
2
20x y
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9rs t
9-2 Prime Factorization
2
20x y
Determine whether each number is prime or composite.
8
8=1 8
8=2 4
The factors of 8 are 1, 2, 4, and 8. Since the number has more than two factors, it is a composite number.
11
11 = 1 11
The number 11 has only two factors, 1 and 11. So, 11 is a prime number.
29
29 = 1 29
The number 29 has only two factors, 1 and 29. So, 29 is a prime number.
26
26 = 1 26
26 = 2 13
The factors of 26 are 1, 2, 13, and 26. Since the number has more than two factors, it is a composite number.
13
13 = 1 13
The number 13 has only two factors, 1 and 13. So, 13 is a prime number.
41
41 = 1 41
The number 41 has only two factors, 1 and 41. So, 41 is a prime number.
57
57 = 1 57
57 = 3 19
The factors of 57 are 1, 3, 19, and 57. Since the number has more than two factors, it is a composite number.
63
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63 = 1 63
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9-2
57 = 1 57
57
= 3 19
Prime
Factorization
The factors of 57 are 1, 3, 19, and 57. Since the number has more than two factors, it is a composite number.
63
63 = 1 63
63 = 3 21
63 = 7 9
The factors of 63 are 1, 3, 7, 9, 21 and 63. Since the number has more than two factors, it is a composite number.
Write the prime factorization of each number. Use exponents for repeated factors.
22
243
105
56
104
196
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9-2 Prime Factorization
196
450
198
ALGEBRA. Factor each monomial.
15y
6n
2
9p
4
11n
3
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18ab
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9p
9-2 Prime Factorization
11n
3
18ab
20qrs
2
24f g
3 2
35c d
GEOMETRY The surface area of a cube is given by the expression 6s2, where s is the side length. Factor 6s2.
REPTILES The graph shows the maximum age in years of the world s longest-lived reptiles. Write the prime
factorization of the age of each reptile.
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9-2 Prime Factorization
REPTILES The graph shows the maximum age in years of the world s longest-lived reptiles. Write the prime
factorization of the age of each reptile.
a. boa constrictor
b. American alligator
c. box turtle
d. Galapagos tortoise
a.
b.
c.
d.
CALENDARS February 3 is a prime day because the month and day (2/3) are represented by prime numbers.
How many prime days are there in a nonleap year?
There are 12 months in a year, and the months Feb., March, May, July, and November all are represented by prime
numbers (2, 3, 5, 7, and 11). March, May and July all have 11 prime number days in their months. November has 10,
and February has 9. All together there are 11 + 11 + 11 + 10 + 9 = 52 prime days in a nonleap year.
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9-2 Prime Factorization
CALENDARS February 3 is a prime day because the month and day (2/3) are represented by prime numbers.
How many prime days are there in a nonleap year?
There are 12 months in a year, and the months Feb., March, May, July, and November all are represented by prime
numbers (2, 3, 5, 7, and 11). March, May and July all have 11 prime number days in their months. November has 10,
and February has 9. All together there are 11 + 11 + 11 + 10 + 9 = 52 prime days in a nonleap year.
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