The document discusses prime numbers and prime factorization. It provides examples of finding the prime factors of numbers like 12, 18, 25, 13, 56, and 100. A prime number is one with exactly two factors, 1 and itself. Prime factorization is dividing a number into its prime factors. For example, the prime factorization of 12 is 2 x 2 x 3. The document asks the reader to find the prime factorizations of several numbers and defines common factors as factors shared between two or more numbers.

1. TARUNGEHLOT
Prime Factorization
What is a prime number? A prime number is a number that has exactly two factors 1
and itself. No, 1 is not a prime number. 1 has exactly one factor 1 X 1 = 1. No, 0 is not a
prime number. 0 has too many factors 0 X 1 = 0, 0 X 50 = 0, 0 multiplied by any number
is still 0. If you start with nothing you cannot multiply to get anything. Yes, 2 is prime. 2
can only be divided into 2 groups of one or one group of 2. Now that you got this idea
started lets try to find the prime numbers in this table below. Numbers can be grouped
to have patterns. If we count by 2, then 2, 4, 6, 8, 10, 12, etc… forms a pattern. Let’s
follow these steps to cross out the numbers that form patterns.
Step 1: Cross out 1, one is not prime.
Step 2: Cross out all multiples of 2 except 2, 2 is prime.
Step 3: Cross out all multiples of 3 except 3, 3 is prime.
Step 4: Cross out all of the multiples of 5 except 5, 5 is prime.
Step 5: Cross all multiples of 7 except 7, 7 is prime.
The numbers not crossed out will be the prime numbers less than 100.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80

2. 81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
1. How many primes are between 1 and 100? ___________________________
2. How many primes other than 2 are even numbers? Explain.
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We have discussed factors and prime numbers. Now let’s put these ideas together and
examine prime factorization. Prime factorization is dividing out the prime numbers from
a product (or number). Let’s look at 12 again. The number 12 has factors of 1,2,3,4,6, &
12. Are any of these numbers primes? Yes, 2 and 3 are primes. Is there anyway that we
can multiply just prime numbers together to have a result of 12? Yes there is.
This process or concept is called prime factorization. There are different ways to divide
a number into its primes.
Way #1 is a factor tree Way #2 is the L method
12 2 12
2 6 2 6
2 x 2 x 3 = 12 3
2 x 2 x 3 = 12
Now, that we have discussed how to find the prime factors of any number. Try
finding the prime factorization of these numbers: 18, 25, 13, 56 and 100.
Use the space below to find the prime factors for these numbers.
18 25
The prime factorization of 18 is____________. The prime factorization of 25 is_____.
13 56

3. 100
It is time for review. What is a prime number? ___________________________
What does prime factorization mean?__________________________________
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Are factors of a number harder to find for some numbers than for others? ______
________________________________________________________________
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What are common factors of a number? You know what a factor is
mathematically. Let’s discuss factors that might be common between two
numbers. Are compatible numbers good examples of numbers that have
common factors? _____ Do multiples of a number have common factors? _____
Do compatible numbers have common factors? ______
Let’s review:
In math class you discussed proper factors. A proper factor is the factors of a
number that do not include the number itself. Below please list the proper factors
of the following numbers: 31, 32, 35, 42, and 100.
31 32 35 42 100
Proper factors: Proper factors: Proper factors: Proper factors: Proper factors:
What is a proper factor of a number? __________________________________
________________________________________________________________
Would numbers with the same proper factors consider these factors common
factors? Why? ___________________________________________________
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