Unit I Review/Study Guide
Things you will need to know:
1.
Understand how to find the prime factorization of numbers.
2.
Understand how to rename numbers written in exponential notation.
3.
Understand how to use a divisibility test (p. 11 S.R.B.) to determine if a number is
divisible by another number.
4.
Understand how to identify prime and composite numbers.
5.
Understand how square numbers and their square roots are related.
6.
Understand how to draw arrays to model multiplication.
7.
Understand how to list the factors of a number.
Make sure you are familiar with your basic multiplication facts as well
as odd and even numbers
Vocabulary
1.
rectangular array:
An arrangement of objects in rows and columns such that each
row has the same number of objects and each column has the same number of objects.
2.
number model:
3.
factor.
One of two or more numbers that are multiplied to give a product. The
numbers that are multiplied are called factors of the product. For example, 4 and 3 are
factors of 12, because 4 x 3 = 12.
4.
product: The result of multiplying two numbers called factors. For example, in 4 x 3
= 12, the product is 12.
A number sentence that models or fits a number story or situation.
5.
factor pair: Two whole number factors of a number whose product is the number. A
number may have more than one factor pair. For example, the factor pairs for 18 are 1
and 18, 2 and 9, and 3 and 6.
6.
even number:
A whole number that can be divided by 2 with no remainder. The
even numbers are 2,4,6,8 and so on.
7.
odd number:
A whole number such as 1,3,5, and so on, that cannot be evenly
divided by 2. When an odd number is divided by 2, there is a remainder.
8.
remainder: An amount left over when one number is divided by another number.
9.
divisible by: One whole number is divisible by another whole number if there is no
remainder when you divide. For example, 28 is divisible by 7 because 28 divided by 7 is
4 with a remainder of 0.
10.
factor rainbow: A way to show factor pairs in a list of all the factors of a number. A
factor rainbow can be used to check whether a list of factors is correct.
prime number: A whole number that has exactly two factors: itself and 1. For
example, 5 is a prime number because its only factors are 5 and 1.
11.
12.
composite number:
A whole number that has more than two factors. For example,
4 is a composite number because it has three factors: 1, 2, and 4.
13.
square number: A number that is the product of a counting number multiplied by
itself. For example, 25 is a square number because 25 = 5 x 5. The numbers are 1, 4, 9,
16, 25, and so on.
14.
exponential notation:
3
A way to show repeated multiplication by the same factor. For
example, 2 is exponential notation for 2 x 2.
15.
square root:
The square root of a number n is a number which, when multiplied by
itself, gives the number n. For example, 4 is the square root of 16 because 4 x 4 = 16.
16.
factor string:
A number written as a product of at least two whole number factors.
For example, a factor string for the number 24 is 2 x 3x 4. This factor string has three
factors, so its length is 3.
17.
prime factorization:
A whole number expressed as a product of prime factors.
Every whole number greater than 1 has a unique prime factorization. For example, the
prime factorization of 24 is 2 x 2 x 2 x 3.
Prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Composite numbers:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21,
22, 24, 25, 26, 27, 28, 30, 32, 33, 34,
35, 36, 38, 39, 40, 42, 44, 45, 46, 48,
49, 50, 51, 52, 54, 55, 56, 57, 58, 60,
62, 63, 64, 65, 66, 68, 69, 70, 72, 74
75, 76, 77, 78, 80, 81, 82, 84, 85, 86
87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
Divisibility Tests:
 All numbers are divisible by 1
 All numbers with a 0, 2, 4, 6, or 8 in the ones place are divisible by 2. They are the
numbers
 Any whole number with 0 in the ones place is divisible by 10
 Any whole number with 0 or 5 in the ones place is divisible by 5
 If the sum of the digits in a whole number is divisible by 3, then the number is divisi
by 3
 If the sum of the digits in a whole number is divisible by 9, then the number is divisi
by 9
 If a whole number is divisible by both 2 and 3, it is divisible by 6
 If the tens and ones digits form a number divisible by 4, then the number is divisible
4
Square numbers and square roots
12=1x1=1
8 2 = 8 x 8 = 64
22=2x2=4
9 2 = 9 x 9 = 81
3 2= 3 x 3 = 9
10 2 = 10 x 10 = 100
4 2 = 4 x 4 = 16
112= 11 x 11 = 121
5 2 = 5 x 5 = 25
12 2 = 12 x 12 = 144
6 2 = 6 x 6 = 36
7 2 = 7 x 7 = 49
Prime factorizations
4=2x2
6=2x3
8=2x2x2
10 = 2 x 5
12 = 2 x 2 x 3
14= 2 x 7
16= 2 x 2 x 2 x 2
18= 2 x 3 x 3
20= 2 x 2 x 5
25= 5 x 5
30= 2 x 3 x 5
35= 5 x 7
40= 2 x 2 x 2 x 5
50= 2 x 5 x 5
100=2 x 5 x 2 x 5