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Prime Numbers and Prime FactorizationPowerPoint Presentation

Prime Numbers and Prime Factorization

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Prime Numbers and Prime Factorization

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Prime Numbers and Prime Factorization

Lesson 3-2

- Factors are the numbers you multiply together to get a product.
- For example, the product 24 has several factors.
- 24 = 1 x 24
- 24 = 2 x 12
- 24 = 3 x 8
- 24 = 4 x 6
- SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24

- Start with 1 times the number.
- Try 2, 3, 4, etc.
- When you repeat your factors, cross out the repeat - you’re done at this point.
- If you get doubles (such as 4 x 4), then you’re done. Repeats or doubles let you know you’re done.

1 x 16

2 x 8

3 x ??

3 is not a factor, so cross it out

4 x 4

doubles = done

The factors of 16 are 1,2,4,8,16

1 x 18

The factors are 1,2,3,6,9,18

2 x 9

3 x 6

4 x ??

5 x ??

6 x 3

Repeat! Cross it out! We’re done!

The only factors of 7 are 1,7

1 x 7

2 x ??

3 x ??

4 x ??

5 x ??

6 x ??

7 x 1

This works, but it is a repeat. We are done.

Prime numbers are

numbers that only have

two factors: one, and the

number itself.

EXAMPLES:

3, 5, 7, 11, 31

Composite numbers

have more than two

factors.

EXAMPLES:

6, 15, 18, 30, 100

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

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

- 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.

- 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…

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.

- 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.

- 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

420

2 x 210

2 x 105

22 x 3 x 5 x 7

3 x 35

5 x 7

54

Answer:

2 x 33