Basic Mathematics for College Students

The prime factorization of a number is given. What is the
number? See Example 9.

APPLICATIONS

101. PERFECT NUMBERS A whole number is
     called aperfect numberwhen the sum of its
     factors that are less than the number equals the
     number. For example, 6 is a perfect number,
     because Find the factors of 28. Then
     use addition to show that 28 is also a perfect
     number.


102. CRYPTOGRAPHY Information is often
     transmitted in code. Many codes involve writing
     products of large primes, because they are difficult
     to factor. To see how difficult, try finding two prime
     factors of 7,663. (Hint:Both primes are greater
     than 70.)


103. LIGHT The illustration shows that the light energy
     that passes through the first unit of area, 1 yard away
     from the bulb, spreads out as it travels away from
     the source. How much area does that energy cover
     2 yards, 3 yards, and 4 yards from the bulb? Express
     each answer using exponents.

1  2  3 6.

23  33  13 23  32  11

32  52 33  53

7  112 2  34

2  3  3  5 2  2  2  7

104. CELL DIVISION After 1 hour, a cell has divided
     to form another cell. In another hour, these two
     cells have divided so that four cells exist. In
     another hour, these four cells divide so that eight
     exist.
     a. How many cells exist at the end of the fourth
     hour?
     b. The number of cells that exist after each division
     can be found using an exponential expression.
     What is the base?
     c. Find the number of cells after 12 hours.

WRITING

105. Explain how to check a prime factorization.


106. Explain the difference between the factorsof a
     number and the prime factorsof a number. Give an
     example.


107. Find and From the results, what can be said
     about any power of 1?


108. Use the phrase infinitely manyin a sentence.

REVIEW

109. MARCHING BANDS When a university band
     lines up in eight rows of fifteen musicians, there are
     five musicians left over. How many band members
     are there?


110. U.S. COLLEGE COSTS In 2008, the average yearly
     tuition cost and fees at a private four-year college
     was $25,143. The average yearly tuition cost and fees
     at a public four-year college was $6,585. At these
     rates, how much less are the tuition costs and fees at
     a public college over four years? (Source: The
     College Board)

12 , 1^3 , 14.

1.8 The Least Common Multiple and the Greatest Common Factor 89

1 yd

2 yd

3 yd

4 yd

1 square unit

As a child, you probably learned how to count by 2’s and 5’s and 10’s. Counting in
that way is an example of an important concept in mathematics called multiples.

SECTION 1.8

The Least Common Multiple and the Greatest

Common Factor

Objectives

1 Find the LCM by listing multiples.

2 Find the LCM using prime

factorization.

3 Find the GCF by listing factors.

4 Find the GCF using prime

factorization.

1 Find the LCM by listing multiples.

The multiplesof a number are the products of that number and 1, 2, 3, 4, 5,and so on.