Download 8-1 Factors and Greatest Common Factors (pp. 524–529)

Vocabulary
greatest common factor . . . . . 525
prime factorization . . . . . . . . . 524
Complete the sentences below with vocabulary words from the list above.
1. A number written as a product so that each of its factors has no factors other than 1
and itself is the
?
.
−−−−−−
2. The
?
of two monomials is the greatest of the factors that the monomials share.
−−−−−−
8-1 Factors and Greatest Common Factors (pp. 524–529)
EXERCISES
EXAMPLES
■
Write the prime factorization of 84.
Write as a product.
Continue until all factors
are prime.
n{
{
Ó
■
Ó£
Ó
Î
Ç
Write the prime factorization of 75.
Keep dividing by prime
factors until the
quotient is 1.
Î Çx
x Óx
x x
£
Write the prime
factorization of
each number.
Find the product
of the common
factors.
The GCF of 36 and 90 is 18.
5
2
Find the GCF of 10x and 4x .
10x 5 = 2 · 5 · x · x · x · x · x
Write the prime
4x 2 = 2 · 2 · x · x
factorization of
each coefficient.
Write powers as
2 · x · x = 2x 2
products.
Find the product
of the common
The GCF of 10x 5 and 4x 2 is 2x 2. factors.
574
Untitled-13 574
6. 23
7. 40
8. 64
9. 66
10. 114
Find the GCF of each pair of numbers.
11. 15 and 50
12. 36 and 132
13. 29 and 30
15. 20 and 48
Find the GCF of 36 and 90.
36 = 2 · 2 · 3 · 3
90 =
2·3·3·5
2 · 3 · 3 = 18
■
5. 32
14. 54 and 81
75 = 3 · 5 · 5 = 3 · 5 2
■
Write the prime factorization of each number.
3. 12
4. 20
Find the GCF of each pair of monomials.
16. 9m and 3
17. 4x and 2x 2
18. -18b 4 and 27b 2
19. 100r and 25r 5
20. A hardware store carries 42 types of boxed nails
and 36 types of boxed screws. The store manager
wants to build a rack so that he can display the
hardware in rows. He wants to put the same
number of boxes in each row, but he wants no
row to contain both nails and screws. What is
the greatest number of boxes that he can display
in one row? How many rows will there be if the
manager puts the greatest number of boxes in
each row?
Chapter 8 Factoring Polynomials
11/8/05 12:01:52 PM