Presentation on theme: "Prime Numbers and Prime Factorization"— Presentation transcript:
1 Prime Numbers and Prime Factorization Lesson 3-2
2 FactorsFactors are the numbers you multiply together to get a product.For example, the product 24 has several factors.24 = 1 x 2424 = 2 x 1224 = 3 x 824 = 4 x 6SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24
3 Finding Factors 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.
4 What are the factors of 16? 1 x 16 2 x 8 3 x ?? 4 x 4 3 is not a factor, so cross it out4 x 4doubles = doneThe factors of 16 are 1,2,4,8,16
5 What are the factors of 18? 1 x 18 The factors are 1,2,3,6,9,18 2 x 9 Repeat! Cross it out! We’re done!
6 What are the factors of 7? The only factors of 7 are 1,7 1 x 7 2 x ?? This works, but it is a repeat. We are done.
7 Prime and Composite Numbers Prime numbers arenumbers that only havetwo factors: one, and thenumber itself.EXAMPLES:3, 5, 7, 11, 31Composite numbershave more than twofactors.EXAMPLES:6, 15, 18, 30, 100
8 A Product of PrimesEvery composite number can be expressed as a product of prime numbers.This is called prime factorization.
9 It can be expressed as a product of primes: 3 x 5 Example15 is a composite number.It can be expressed as a product of primes: 3 x 5
10 To 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.
12 Example: Prime Factorization of 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 5025 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 25Both numbers are prime, leaving us with all primes.5 x 5
13 What’s the Answer?Now, we just list our factors with multiplication signs between them. Use the circled prime numbers.2 x 2 x 5 x 5We have listed 100 as a product of prime numbers.
14 Exponent FormWe 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: 225 x 5 can be expressed as 52Put it together, and 2 x 2 x 5 x 5 is more simply put as22 x 52
15 Another Example4202 x 2102 x 10522 x 3 x 5 x 73 x 355 x 7
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