Title: Prime Factorization
1Prime Factorization
2A Product of Primes
- Every composite number can be expressed as a
product of prime numbers. - This is called prime factorization.
3Example
- 15 is a composite number.
- It can be expressed as a product of primes 3 x 5
4To find the prime factorization
- Divide the number by the first prime number
possible. - Circle the prime number, and continue with the
other factor. - Divide the new factor by a prime number.
- Continue this process until the only numbers you
have left are prime numbers.
5Remember 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
6Example 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.
7Whats 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.
8Exponent 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
9Another Example
420
2 x 210
2 x 105
22 x 3 x 5 x 7
3 x 35
5 x 7
10Try this on your own
54
Answer
2 x 33
11Homework Time!