Basic Mathematics for College Students

98 Chapter 1 Whole Numbers

b.How many of each type of

item will be in each gift pack?

Now TryProblem 93

Solution

a.To find the GCF, we prime factor and 42, and circle the prime factors

that they have in common.

The GCF is the product of the circled numbers.

The florist can make 6 identical arrangements from the tulips.

b.To find the number of white, pink, and purple tulips in each of the

6 arrangements, we divide the number of tulips of each color by 6.

White tulips: Pink tulips: Purple tulips:

Each of the 6 identical arrangements will contain 2 white tulips, 5 pink tulips,

and 7 purple tulips.

42

6

 7

30

6

 5

12

6

 2

GCF (12, 30, 42) 2  3  6

42  2  3  7

30  2  3  5

12  2  2  3

12, 30,

1. 
   
   
   
   2. 40 3. 24 4. 288 5. 900 6.180 days 7. 6 8. 12
   
   
   
   


2. 1 10. 15 11. a.18 gift packs b.2 markers, 3 pencils, 6 pens

9, 18, 27, 36, 45, 54, 63, 72

ANSWERS TO SELF CHECKS

VOCABULARY

Fill in the blanks.

1. The of a number are the products of that
   number and and so on.


2. Because 12 is the smallest number that is a multiple of
   both 3 and 4, it is the of
   3 and 4.


3. One number is by another if, when dividing
   them, we get a remainder of 0.


4. Because 6 is the largest number that is a factor of both
   18 and 24, it is the of
   18 and 24.

CONCEPTS

5. a. The LCM of 4 and 6 is 12. What is the smallest
   whole number divisible by 4 and 6?
   b. Fill in the blank: In general, the LCM of two whole
   numbers is the whole number that is
   divisible by both numbers.


6. a. What are the common multiples of 2 and 3 that
   appear in the list of multiples shown in the next
   column?

1, 2, 3, 4, 5,

b. What is the LCM of 2 and 3?

Multiples of 2 Multiples of 3

7. a.The first six multiples of 5 are
   and 30. What is the first multiple of 5 that is
   divisible by 4?
   b. What is the LCM of 4 and 5?


8. Fill in the blanks to complete the prime factorization
   of 24.


9. The prime factorizations of 36 and 90 are:
   36  2  2  3  3
   90  2  3  3  5

24

4

2

5, 10, 15, 20, 25,

2  6  12 3  6  18

2  5  10 3  5  15

2  4  8 3  4  12

2  3  6 3  3  9

2  2  4 3  2  6

2  1  2 3  1  3

SECTION 1.8 STUDY SET