Prime Factorization

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Prime Factorization

• Lesson 4.2

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A Product of Primes

• Every composite number can be expressed as a
  product of prime numbers.
• This is called prime factorization.

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Example

• 15 is a composite number.
• It can be expressed as a product of primes 3 x 5

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To find the prime factorization

1. Divide the number by the first prime number
   possible.
2. Circle the prime number, and continue with the
   other factor.
3. Divide the new factor by a prime number.
4. Continue this process until the only numbers you
   have left are prime numbers.

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Remember the Prime Number List

• 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

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Example Prime Factorization of 100.
100
100 2 50. Two is the first prime number that
goes into 100.
Now we deal with the 50. Divide it by 2 to get
the next factors.
2 is a prime number, so we are done with it.
2 X 50
25 is not divisible by the first prime, 2. The
next prime, 3, does not work either. We must
divide by 5 to get a factor.
2 X 25
5 x 5
Both numbers are prime, leaving us with all
primes.
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Whats the Answer?

• Now, we just list our factors with multiplication
  signs between them. Use the circled prime
  numbers.
• 2 x 2 x 5 x 5
• We have listed 100 as a product of prime numbers.

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Exponent Form

• We have just listed our prime factorization for
  100 as being 2 x 2 x 5 x 5. This is repeated
  multiplication. Repeated multiplication can be
  expressed with exponents.
• Our prime numbers are our bases. The number of
  times the prime number is written is the
  exponent.
• 2 x 2 can be expressed in exponent form 22
• 5 x 5 can be expressed as 52
• Put it together, and 2 x 2 x 5 x 5 is more simply
  put as
• 22 x 52

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Another Example
420
2 x 210
2 x 105
22 x 3 x 5 x 7
3 x 35
5 x 7
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Try this on your own
54
Answer
2 x 33
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Homework Time!