Unit: Fractions
Topic: Greatest Common Factor, Least Common Multiple and Prime Factorization
Even number: any number that can be divided by 2. All even numbers end in 2,4,6,8 or 0.
Odd numbers: any number that cannot be divided by 2
Prime number: an integer whose only factors are 1 and itself (2 is the only even prime number)
Composite number: any integer that can be divided by at least one other number (a factor) other than itself
Multiple: the product of two whole numbers is a multiple of each those numbers
Examplemultiples of 3: 3,6,9,12
Factors: a number that can divide another number without a remainder
Example  factors of 12: 1,2,3,4,6,12
Factoring: a number involves breaking it down into smaller numbers that can be multiplied together to get the original
number
Greatest common factor- of two numbers is the largest factor shared by both. You determine the GCF by calculating
all the factors of both numbers and finding the largest one that is a factor of both.
Relatively prime: two or more numbers that only have 1 as their greatest common factor (example: 15 and 32 are
relatively prime because their GCF is 1).
Least common multiple- of two numbers is the smallest number (not including zero or one) that is a multiple of both.
The LCM of two numbers is always larger than either number.
Prime factors: an expression of numbers that divides another integer without a remainder where all the factors are
prime
Prime factorization: breaks down a number’s factors into prime numbers. This can be done using factor trees.
*Numbers circled are prime numbers.
Prime Numbers 1-100 Chart
Here's a chart with all the numbers from 1-100:
Number Is it Prime? Explanation
1
No
1 is neither prime nor composite. It's a special number.
2
Yes
2 is divisible by itself and 1.
3
Yes
3 is divisible by itself and 1.
4
No
4 is divisible by 2, so it's not prime.
5
Yes
5 is divisible by itself and 1.
6
No
6 is divisible by 2 and 3, so it's not prime.
7
Yes
7 is divisible by itself and 1.
8
No
8 is divisible by 2, so it's not prime.
9
No
9 is divisible by 3, so it's not prime.
10
No
10 is divisible by 2 and 5, so it's not prime.
11
Yes
11 is divisible by itself and 1.
12
No
12 is divisible by 2 and 3, so it's not prime.
13
Yes
13 is divisible by itself and 1.
14
No
14 is divisible by 2 and 7, so it's not prime.
15
No
15 is divisible by 3 and 5, so it's not prime.
16
No
16 is divisible by 2, so it's not prime.
17
Yes
17 is divisible by itself and 1.
18
No
18 is divisible by 2 and 3, so it's not prime.
19
Yes
19 is divisible by itself and 1.
20
No
20 is divisible by 2 and 5, so it's not prime.
21
No
21 is divisible by 3 and 7, so it's not prime.
22
No
22 is divisible by 2 and 11, so it's not prime.
23
Yes
23 is divisible by itself and 1.
24
No
24 is divisible by 2 and 3, so it's not prime.
25
No
25 is divisible by 5, so it's not prime.
26
No
26 is divisible by 2 and 13, so it's not prime.
27
No
27 is divisible by 3, so it's not prime.
28
No
28 is divisible by 2 and 7, so it's not prime.
29
Yes
29 is divisible by itself and 1.
30
No
30 is divisible by 2, 3, and 5, so it's not prime.
31
Yes
31 is divisible by itself and 1.
32
No
32 is divisible by 2, so it's not prime.
33
No
33 is divisible by 3 and 11, so it's not prime.
34
No
34 is divisible by 2 and 17, so it's not prime.
35
No
35 is divisible by 5 and 7, so it's not prime.
36
No
36 is divisible by 2 and 3, so it's not prime.
37
Yes
37 is divisible by itself and 1.
38
No
38 is divisible by 2 and 19, so it's not prime.
39
No
39 is divisible by 3 and 13, so it's not prime.
40
No
40 is divisible by 2 and 5, so it's not prime.
41
Yes
41 is divisible by itself and 1.
42
No
42 is divisible by 2, 3, and 7, so it's not prime.
43
Yes
43 is divisible by itself and 1.
44
No
44 is divisible by 2 and 11, so it's not prime.
45
No
45 is divisible by 3 and 5, so it's not prime.
46
No
46 is divisible by , so it's not prime.
47
Yes
47 is divisible by itself and 1.
48
No
48 is divisible by 2 and 3, so it's not prime.
49
No
49 is divisible by 7, so it's not prime.
50
No
50 is divisible by 2 and 5, so it's not prime.
51
No
51 is divisible by 3 and 17, so it's not prime.
52
No
52 is divisible by 2 and 13, so it's not prime.
53
Yes
53 is divisible by itself and 1.
54
No
54 is divisible by 2 and 3, so it's not prime.
55
No
55 is divisible by 5 and 11, so it's not prime.
56
No
56 is divisible by 2 and 7, so it's not prime.
57
No
57 is divisible by 3 and 19, so it's not prime.
58
No
58 is divisible by 2 and 29, so it's not prime.
59
Yes
59 is divisible by itself and 1.
60
No
60 is divisible by 2, 3, and 5, so it's not prime.
61
Yes
61 is divisible by itself and 1.
62
No
62 is divisible by 2 and 31, so it's not prime.
63
No
63 is divisible by 3 and 7, so it's not prime.
64
No
64 is divisible by 2, so it's not prime.
65
No
65 is divisible by 5 and 13, so it's not prime.
66
No
66 is divisible by 2, 3, and 11, so it's not prime.
67
Yes
67 is divisible by itself and 1.
68
No
68 is divisible by 2 and 17, so it's not prime.
69
No
69 is divisible by 3 and 23, so it's not prime.
70
No
70 is divisible by 2, 5, and 7, so it's not prime.
71
Yes
71 is divisible by itself and 1.
72
No
72 is divisible by 2 and 3, so it's not prime.
73
Yes
73 is divisible by itself and 1.
74
No
74 is divisible by 2 and 37, so it's not prime.
75
No
75 is divisible by 3 and 5, so it's not prime.
76
No
76 is divisible by 2 and 19, so it's not prime.
77
No
77 is divisible by 7 and 11, so it's not prime.
78
No
78 is divisible by 2, 3, and 13, so it's not prime.
79
Yes
79 is divisible by itself and 1.
80
No
80 is divisible by 2 and 5, so it's not prime.
81
No
81 is divisible by 3, so it's not prime.
82
No
82 is divisible by 2 and 41, so it's not prime.
83
Yes
83 is divisible by itself and 1.
84
No
84 is divisible by 2, 3 and 7, so it's not prime.
85
No
85 is divisible by 5 and 17, so it's not prime.
86
No
86 is divisible by 2 and 43, so it's not prime.
87
No
87 is divisible by 3 and 29, so it's not prime.
88
No
88 is divisible by 2 and 11, so it's not prime.
89
Yes
89 is divisible by itself and 1.
90
No
90 is divisible by 2, 3, and 5, so it's not prime.
91
No
91 is divisible by 7 and 13, so it's not prime.
92
No
92 is divisible by 2 and 23, so it's not prime.
93
No
93 is divisible by 3 and 31, so it's not prime.
94
No
94 is divisible by 2 and 47, so it's not prime.
95
No
95 is divisible by 5 and 19, so it's not prime.
96
No
96 is divisible by 2 and 3, so it's not prime.
97
Yes
97 is divisible by itself and 1.
98
No
98 is divisible by 2 and 7, so it's not prime.
99
No
99 is divisible by 3 and 11, so it's not prime.
100
No
100 is divisible by 2 and 5, so it's not prime.
Greatest Common Factor (GCF)
*Using Prime factorization to show GCF
The prime factors of 36: 2 X 2 X 3 X 3
The prime factorization of 24: 2 X 3 X 3 X 3
List the factors that both numbers share: 2, 3 , 3
Multiply shared factors: 2X3X3= 18
*Always write factors from smallest to largest
*Once
you have
a prime
number,
you stop
Greatest
common
factorof two
numbers
is thefactoring
largest factor shared by both. You determine the GCF by calculating
all the factors of both numbers and finding the largest one that is a factor of both.
*No matter how you break up a number, the prime factors always end up the same
Relatively prime: two or more numbers that only have 1 as their greatest common factor (example: 15 and 32 are
relatively prime because their GCF is 1).
*Using factor Method to show GCF
Example: What is the GCF of 44 and 66 by using the factor method (listing)?
Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 66: 1, 2, 3, 11, 22, 33, 66
The greatest common factor of 44 and 66 is 22.
Least Common Multiple (LCM)
Least common multiple- of two numbers is the smallest number (not including zero or one) that is a multiple
of both. The LCM of two numbers is always larger than either number.
One way to find LCM is to list the multiples of each number until you find the first one they have in common.
Example: 6 and 8
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 8: 8, 16, 24
LCM= 24
Another way to find LCM is to write the prime factorization of each number. Multiply all factors together.
Use common factors only once (in other words, use the highest exponent for a repeated factor).
Example:
Additional Resources:
https://learnzillion.com/lesson_plans/5128-find-the-gcf-and-lcm-using-prime-factorization
http://www.mathplayground.com/howto_gcflcm.html
https://www.ixl.com/math/grade-6/gcf-and-lcm-word-problems
http://mathforum.org/library/drmath/sets/select/dm_lcm_gcf.html