Download Chapter 2 Study Guide

Chapter 2 Study Guide
Vocabulary Words (Quizzes will include vocabulary words)
Prime Factorization- the expression of a composite number as a product of prime numbers. (P. 53) This string
of numbers is the so-called answer to a “factor tree” problem.
Example: 2 𝑥 52 = 50
Associative Property of Multiplication- states that changing the grouping of the factors in a multiplication
statement does not change the product. (P. 54)
For any number a, b, and c, (a x b) x c = a x (b x c)
If a = 2, b = 3, c = 6 then
(2 x 3) x 6 = 2 x (3 x 6)
Fundamental Theorem of Arithmetic- states that every natural number is either prime or can be uniquely
written as a product of primes. (P. 58)
This simply means that every number is prime OR you can make it a group of prime numbers
Powers- used to express a repeated factor. The base of a power is the factor and the exponent of the power is
the number of times the factor is repeated. (P. 57)
Base of the power- the factor that is multiplied repeatedly in the power. (P. 57)
Exponent of the power- the number of time the base is used as a factor of repeated multiplication. (P. 57)
3x3x3x3x3
35
In this problem the base is 3 and the exponent is 5
You read it, 3 to the power of 5.
Factor Tree- is a way to organize and help you determine the prime factorization of a number. (P. 55)
*There is an example on page 55.
Example factor tree for 18
18
2 x 9
2x3x3
18= 2 x 32
2 is a prime number, 9 is a composite number
2 is prime, 3 is prime
The product 18 needs to be written as a prime factorization
Common Multiple- a number that is a multiple of two or more numbers. (P. 72)
Relatively Prime Numbers- two numbers that do not have any common factors other than 1. (P. 74)
Example: 8 and 9
Factors of 8= 1, 2, 4, 8
Factors of 9= 1, 3, 9
The number 8 and 9 have factors but these numbers only share the number 1 as a common factor.
GCF (Greatest Common Factor) (P. 72)
15 and 30:
1. Write out all the factors of 15.
2.
Write out all the factors of 30.
15______
1 x 15
3x5
______30_______
1 x 30
2 x 15
3 x 10
5x6
Find the Greatest factor that 15 and 30 have in common.
GCF of 15 and 30 is 15
The Least Common Multiple (LCM)- is the smallest multiple that two or more numbers have in common.
(P. 63)
*The LCM is the product of the greatest power of each prime factor as they appear in any of the prime
factorizations.
Example: Find the LCM of 10 and 6
Write out the multiples of the first number: 10
10, 20, 30, 40, 50, 60, 70, 80, 90
Write out the multiples of the second number: 6 =6, 12, 18, 24, 30, 36, 42, 48, 54, 60
What are the COMMON Multiples of 6 and 10? 30, 60, 90
What is the Lowest Multiple that 10 and 6 have in common?
LCM of 10 and 6 is 30
Using GCF and LCM to Solve Problems- see page 91 in student textbook as well as 2.4.
Note: The math book provides a chapter 2 summary on pages 89-91.