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Vocabulary for Unit 1
Vocabulary for Unit 1
Prime Number – A number greater than 1 that has only 2
factors, 1 and itself.
Composite Number – A number that has 3 or more factors.
Factor – A number that divides evenly into another number
without a remainder.
Greatest Common Factor (GCF) – The largest number that
is a factor for 2 or more numbers.
Multiple – The product of a number and any other whole
number.
Least Common Multiple (LCM) – The smallest number that is
a multiple of 2 or more numbers.
Factor Tree – A diagram used to decompose a composite
number into its prime factorization.
Prime Factorization – An expression of a whole number as a
product of prime numbers.
Exponent – The number of times a base number is multiplied
by itself.
Prime Number – A number greater than 1 that has only 2
factors, 1 and itself.
Composite Number – A number that has 3 or more factors.
Factor – A number that divides evenly into another number
without a remainder.
Greatest Common Factor (GCF) – The largest number that
is a factor for 2 or more numbers.
Multiple – The product of a number and any other whole
number.
Least Common Multiple (LCM) – The smallest number that is
a multiple of 2 or more numbers.
Factor Tree – A diagram used to decompose a composite
number into its prime factorization.
Prime Factorization – An expression of a whole number as a
product of prime numbers.
Exponent – The number of times a base number is multiplied
by itself.
3 4
16 17
29 30
42 43
7
20
33
46
8
21
34
47
9
22
35
48
10
23
36
49
11
24
37
50
Prime and Composite Numbers
5 6
18 19
31 32
44 45
12
25
38
51
13
26
39
52
14
27
40
53
2
15
28
41
3 4
16 17
29 30
42 43
5 6
18 19
31 32
44 45
7
20
33
46
8
21
34
47
9
22
35
48
10
23
36
49
11
24
37
50
12
25
38
51
13
26
39
52
14
27
40
53
Then go to the next remaining number after 2. Circle it and cross out all its multiples
other than itself. Repeat until every number is either circled or crossed out.
Step 2
Circle 2 and cross out all multiples of 2 other than the number 2.
Step 1
2
15
28
41
Then go to the next remaining number after 2. Circle it and cross out all its multiples
other than itself. Repeat until every number is either circled or crossed out.
Step 2
Circle 2 and cross out all multiples of 2 other than the number 2.
Step 1
Prime and Composite Numbers
These are prime numbers.
47
23
7
31
These are prime numbers.
101
59
13
29
67
5
11
3
23
These are composite numbers.
87
33
14
27
16
9
25
15
2
4
19
110
6
1
25
18
61
What is a prime number?
What is a composite number?
31
57
111
87
33
Circle the prime numbers. Underline the composite numbers.
2
7
101
59
13
29
67
5
11
3
These are composite numbers.
51
22
47
27
51
16
22
9
25
15
2
4
Circle the prime numbers. Underline the composite numbers.
0
90
14
2
19
110
6
1
25
18
61
What is a prime number?
What is a composite number?
57
111
0
90
Divisibility Rules
2:
If the last digit is even (0, 2, 4, 6, or 8).
24 – yes
3:
30 – yes
Divisibility Rules
2:
67 - no
If the sum of the digits is divisible by 3.
24 – yes
3:
57: 5 + 7 = 12 & 12 is divisible by 3
4:
If the last 2 digits are divisible by 4.
 132: 32 ÷ 4 = 8
5:
85 – yes
6:
120 – yes
4:
5:
If the sum of the digits is divisible by 9.
585: 5 + 8 + 5 = 18 & 18 is divisible by 9
10: If the last digit is 0.
90 – yes
680 – yes
If the last 2 digits are divisible by 4.
6:
X 226: 26 ÷ 4 = 6.5
If the last digit is 0 or 5.
85 – yes
54: 5 + 4 = 9 & 9 is divisible by 3
9:
67 - no
If the sum of the digits is divisible by 3.
 132: 32 ÷ 4 = 8
53 - no
If the number is divisible by 2 AND 3.
30 – yes
57: 5 + 7 = 12 & 12 is divisible by 3
X 226: 26 ÷ 4 = 6.5
If the last digit is 0 or 5.
If the last digit is even (0, 2, 4, 6, or 8).
120 – yes
53 - no
If the number is divisible by 2 AND 3.
54: 5 + 4 = 9 & 9 is divisible by 3
9:
If the sum of the digits is divisible by 9.
585: 5 + 8 + 5 = 18 & 18 is divisible by 9
10: If the last digit is 0.
104- no
90 – yes
680 – yes
104- no
Factor Notes
Factor Notes
 1 is a factor of every number.
 1 is a factor of every number.
 0 is NEVER a factor of any number because
 0 is NEVER a factor of any number because
numbers cannot be divided by 0.
numbers cannot be divided by 0.
Examples:
Examples:
Factors of 12: 1, 2, 3,
4, 6, 12
Factors of 12: 1, 2, 3,
4, 6, 12
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
 When would I need to use factors?
 When would I need to use factors?
A large group of people want to split up to make
A large group of people want to split up to make
smaller groups to walk around an amusement park.
smaller groups to walk around an amusement park.
What are the possibilities if the group is 18?
What are the possibilities if the group is 18?
Greatest Common Factor (GCF) – The largest
Greatest Common Factor (GCF) – The largest
number that is a factor for 2 or more numbers.
number that is a factor for 2 or more numbers.
What is the GCF of 16 and 24?
What is the GCF of 16 and 24?
16:
1, 2, 4, 8, 16
16:
1, 2, 4, 8, 16
24:
1, 2, 3, 4, 6, 8, 12, 24
24:
1, 2, 3, 4, 6, 8, 12, 24
Common Factors are 1, 2, 4, 8
Common Factors are 1, 2, 4, 8
8 is the GCF
8 is the GCF
What is the GCF of 20 and 40?
What is the GCF of 20 and 40?
20:
1, 2, 4, 5, 10, 20
20:
1, 2, 4, 5, 10, 20
40:
1, 2, 4, 5, 8, 10, 20, 40
40:
1, 2, 4, 5, 8, 10, 20, 40
Common Factors are 1, 2, 4, 5, 10, 20
Common Factors are 1, 2, 4, 5, 10, 20
20 is the GCF
20 is the GCF
If the GCF is 1, then the numbers are relatively prime.
If the GCF is 1, then the numbers are relatively prime.
Ex.
15: 1, 3, 5, 15
8:
1, 2, 4, 8
Ex.
15: 1, 3, 5, 15
8:
1, 2, 4, 8
Multiple – The product of a number and any other whole
Multiple – The product of a number and any other whole
number.
number.
Multiples of 6 are 6, 12, 18, 24, 30 and so on….
Multiples of 6 are 6, 12, 18, 24, 30 and so on….
How can I check to see if a number is a multiple of another
How can I check to see if a number is a multiple of another
number? Divide! No remainder = Multiple
number? Divide! No remainder = Multiple
24
24
Ex. 6 144
Ex. 6 144
-12
So, 144 is a multiple of 6.
-12
So, 144 is a multiple of 6.
24
24
-24
-24
0
0
Least Common Multiple (LCM) – The smallest number
Least Common Multiple (LCM) – The smallest number
that is a multiple of 2 or more numbers.
that is a multiple of 2 or more numbers.
What is the LCM of 8 and 12?
What is the LCM of 8 and 12?
Multiples of 8:
8, 16, 24, 32, 40, 48. . .
Multiples of 8:
8, 16, 24, 32, 40, 48. . .
Multiples of 12:
12, 24, 36, 48. . .
Multiples of 12:
12, 24, 36, 48. . .
LCM is 24
LCM is 24
What is the LCM of 5 and 15?
What is the LCM of 5 and 15?
Multiples of 5:
5, 10, 15, 20, 25, 30, 35. . .
Multiples of 5:
5, 10, 15, 20, 25, 30, 35. . .
Multiples of 15:
15, 30 . . .
Multiples of 15:
15, 30 . . .
LCM is 15
LCM is 15
Prime Factorization – An expression of a whole number as a
Prime Factorization – An expression of a whole number as a
product of prime numbers.
product of prime numbers.
Ex. 2 x 2 x 2 x 5 = 40
Ex. 2 x 2 x 2 x 5 = 40
2 x 2 x 2 x 5 can also be written as 23 x 5
2 x 2 x 2 x 5 can also be written as 23 x 5
23
power
Exponent
23
power
base
Exponent
base
Exponent – The number of times a base number is multiplied
Exponent – The number of times a base number is multiplied
by itself.
by itself.
52 = 5 x 5 = 25
34 = 3 x 3 x 3 x 3 = 81
52 = 5 x 5 = 25
34 = 3 x 3 x 3 x 3 = 81
You can find the prime factorization of a number using a
You can find the prime factorization of a number using a
factor tree.
factor tree.
Factor Tree – A diagram used to decompose a composite
Factor Tree – A diagram used to decompose a composite
number into its prime factorization.
number into its prime factorization.
40
4
x 10
2 x 2x 2 x 5
40
40
5 x 8
2 x 4
4
x 10
2 x 2x 2 x 5
40
5 x 8
2 x 4
2 x 2
Prime factorization of 40 is 23 x 5.
2 x 2
Prime factorization of 40 is 23 x 5.
Finding the GCF using Factor Trees
Finding the GCF using Factor Trees
Step 1: Complete factor trees for each number.
Step 1: Complete factor trees for each number.
Step 2: Write down the prime factors they have in common.
Step 2: Write down the prime factors they have in common.
Step 3: Multiply the common prime factors to get the GCF.
Step 3: Multiply the common prime factors to get the GCF.
What is the GCF of 36 and 24?
What is the GCF of 36 and 24?
36
4
24
x 9
4
2 x 2x 3 x 3
x
36
6
2 x 2x 2 x 3
x 9
4
2 x 2x 3 x 3
2x2x3x3
2x2x2x3
2x2x2x3
GCF = 12
What is the GCF of 55 and 66?
2 x 2 x 3 = 12
66
6
GCF = 12
x
55
11
5
66
x 11
6
2 x 3
x
11
2 x 3
5 x 11
2 x 3 x 11
6
What is the GCF of 55 and 66?
55
x 11
x
2 x 2x 2 x 3
2x2x3x3
2 x 2 x 3 = 12
5
4
24
5 x 11
GCF = 11
2 x 3 x 11
GCF = 11
Finding the LCM using Prime Numbers
Finding the LCM using Prime Numbers
Step 1: Write the numbers you are trying to find the LCM.
Step 1: Write the numbers you are trying to find the LCM.
Step 2: Draw a line under the numbers and down the left side.
Step 2: Draw a line under the numbers and down the left side.
Step 3: Beginning with the smallest prime number that will divide
into a number, divide.
Step 3: Beginning with the smallest prime number that will divide
into a number, divide.
Step 4: Continue dividing by the smallest prime number until
both columns end in a 1.
Step 4: Continue dividing by the smallest prime number until
both columns end in a 1.
Step 5: Multiply all the prime numbers on the left side.
Step 5: Multiply all the prime numbers on the left side.
What is the LCM of 36 and 24?
36
24
What is the LCM of 36 and 24?
36
24
2
18
12
2
18
12
2
9
6
2
9
6
2
9
3
2
9
3
3
3
1
3
3
1
3
1
3
1
2 x 2 x 2 x 3 x 3 = 72
2 x 2 x 2 x 3 x 3 = 72
LCM = 72
LCM = 72
What is the LCM of 22 and 66?
22
66
What is the LCM of 22 and 66?
22
66
2
11
33
2
11
33
3
11
11
3
11
11
11
1
1
11
1
1
2 x 3 x 11 = 66
LCM = 66
2 x 3 x 11 = 66
LCM = 66
Finding the LCM using Factor Trees
Finding the LCM using Factor Trees
Step 1: Complete factor trees for each number.
Step 1: Complete factor trees for each number.
Step 2: Write down the prime factors they have in common.
Step 2: Write down the prime factors they have in common.
Step 3: Write down any remaining prime numbers.
Step 3: Write down any remaining prime numbers.
Step 4: Multiply the numbers to get the LCM.
Step 4: Multiply the numbers to get the LCM.
What is the LCM of 36 and 24?
36
What is the LCM of 36 and 24?
36
4
x 9
24
4
2 x 2x 3 x 3
x
6
2 x 2x 2 x 3
x 9
4
2 x 2x 3 x 3
2x2x3x3
2x2x2x3
2x2x2x3
What is the LCM of 22 and 66?
22
x 11
LCM = 72
6
x
11
2
x 11
2 x 11
2 x 3 x 11
2 x 3 x 11
LCM = 66
x
2 x 3
2 x 11
2 x 11 x 3 = 66
LCM = 72
66
6
2 x 3
2 x 11 x 3 = 66
6
2 x 2 x 3 x 2 x 3= 72
What is the LCM of 22 and 66?
22
66
x
2 x 2x 2 x 3
2x2x3x3
2 x 2 x 3 x 2 x 3= 72
2
4
24
LCM = 66
11