Chapter 1 Summary and Review 123SECTION 1.7 Prime Factors and Exponents
Numbers that are multiplied together are
called factors.
To factora whole number means to express it
as the product of other whole numbers.
If a whole number is a factor of a given
number, it also divides the given number
exactly.DEFINITIONS AND CONCEPTS EXAMPLES
The pairs of whole numbers whose product is 6 are:
and
From least to greatest, the factors of 6 are and 6.
Each of the factors of 6 divides 6 exactly (no remainder):
6
61
6
3
2
6
2
3
6
1
6
1, 2, 3,
1 6 6 2 3 6
- WEIGHT TRAINING For part of a woman’s
upper body workout, she does 1 set of twelve
repetitions of 75 pounds on a bench press
machine. How many total pounds does she lift in
that set? - PARKING Parking lot B4 at an amusement park
opens at 8:00 AMand closes at 11:00 PM. It costs
$5 to park in the lot. If there are twenty-four rows
and each row has fifty parking spaces, how many
cars can park in the lot? - PRODUCTION A manufacturer produces
15,000 light bulbs a day. The bulbs are packaged 6 to
a box. How many boxes of light bulbs are produced
each day?
84. EMBROIDERED CAPS A digital embroidery
machine uses 16 yards of thread to stitch a team
logo on the front of a baseball cap. How many hats
can be embroidered if the thread comes on spools of
1,100 yards? How many yards of thread will be left
on the spool?
85. FARMING In a shipment of 350 animals, 124 were
hogs, 79 were sheep, and the rest were cattle. Find
the number of cattle in the shipment.
86. HALLOWEEN A couple bought 6 bags of mini
Snickers bars. Each bag contains 48 pieces of candy.
If they plan to give each trick-or-treater 3 candy
bars, to how many children will they be able to give
treats?
If a whole number is divisible by 2, it is called
an evennumber.
If a whole number is not divisible by 2, it is
called an oddnumber.Even whole numbers: ...Odd whole numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19,...0, 2, 4, 6, 8, 10, 12, 14, 16, 18,
A prime numberis a whole number greater
than 1 that has only 1 and itself as factors.
There are infinitely many prime numbers.Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,...The composite numbersare whole numbers
greater than 1 that are notprime. There are
infinitely many composite numbers.Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18,...To find the prime factorizationof a whole
number means to write it as the product of
only prime numbers.
A factor treeand a division laddercan be used
to find prime factorizations.Use a factor tree to find the prime factorization of 30.Factor each number that is encountered as a
product of two whole numbers (other than 1 and
itself) until all the factors involved are prime.The prime factorization of 30 is
Use a division ladder to find the prime factorization of 70.Perform repeated divisions by prime numbers until
the final quotient is itself a prime number.The prime factorization of 70 is 2 5 7.(^2) 70
5 35
7