factors, primes & composite numbers. definition product – an answer to a multiplication...
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Factors, Primes & Composite Numbers
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Definition
Product – An answer to a multiplication problem.
7 x 8 = 56Product
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Definition
Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors
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Definition
Factor – a number that divides evenly into another.
56 ÷ 8 = 7
Factor
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What are the factors?
6 x 7 = 427 x 9 = 638 x 6 = 484 x 9 = 36
6 & 77 & 98 & 64 & 9
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What are the factors?
42 ÷ 7 = 663 ÷ 9 = 748 ÷ 6 = 836 ÷ 9 = 4
7969
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Definition Prime Number – a number
that has only two factors, itself and 1.
77 is prime because the only numbers
that will divide into it evenly are 1 and 7.
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Examples of Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19
Special Note:One is not a prime number.
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Definition Composite number – a
number that has more than two factors.
8The factors of 8 are 1, 2, 4, 8
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Examples of Composite Numbers
4, 6, 8, 9, 10, 12, 14, 15
Special Note:Every whole number from 2 on is
either composite or prime.
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Our Lonely 1
Special Note:One is not a prime nor a composite number.
It is not primebecause it doesnot have exactly
two differentfactors.
It is not composite
because it doesnot have morethan 2 factors.
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Definition Prime Factorization – A way
to write a composite number as the product of prime factors.
2 x 2 x 3 = 12or
2 x 3 = 122
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How to Do Prime Factorization Using a Factor Tree
48Step 1 – Start with a composite number.
Step 2 – Write down a multiplication problem that equals this number orany pair of factors of this number.
6 x 8 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 3 – Find factors of these factors.
6 x 8 = 48
2 x 3 x 2 x 4 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 4 – Find factors of these numbersuntil all factors are prime numbers.
6 x 8 = 482 x 3 x 2 x 4 = 48
2 x 3 x 2 x 2 x 2 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 5 – Write the numbers from leastto greatest.
6 x 8 = 482 x 3 x 2 x 2 x 2 = 482 x 2 x 2 x 2 x 3 = 48
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How to Do Prime Factorization Using a Factor Tree
Step 6 – Count how many numbers arethe same and write exponents for them.
6 x 8 = 482 x 3 x 2 x 2 x 2 = 482 x 2 x 2 x 2 x 3 = 48 2 x 3 = 484
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Prime factor this number
42 x 2
2 = 42
= 4
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Prime factor this number
62 x 3 = 6
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Prime factor this number
82 x 4
2 = 83
= 82 x 2 x 2 = 8
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Prime factor this number
93 x 3 = 9
3 = 92
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Prime factor this number
102 x 5 = 10
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Prime factor this number
123 x 4
2 x 3 = 122
= 123 x 2 x 2 = 122 x 2 x 3 = 12
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Prime factor this number
142 x 7 = 14
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Prime factor this number
153 x 5 = 15
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Prime factor this number
164 x 4
2 = 164
= 162 x 2 x 2 x 2 = 16
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Prime factor this number
183 x 6
2 x 3 = 182
= 183 x 2 x 3 = 182 x 3 x 3 = 18
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Prime factor this number
204 x 5
2 x 5 = 202
= 202 x 2 x 5 = 20
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Prime factor this number
213 x 7 = 21
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Prime factor this number
222 x 11= 22
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What about those with variables?
24y2
We do the same as before, we just add the variables with it
2 * 2 * 2 * 3 * y * y23 * 3 * y2
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4-5 Greatest Common Factor
Examplea. Use prime factorization to find the GCF of 42 and 70.
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4-5 Greatest Common Factor
Examplea. Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.42 = 7 * 6 70 = 7 * 10
![Page 34: Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e605503460f94b5a46c/html5/thumbnails/34.jpg)
4-5 Greatest Common Factor
Examplea. Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.42 = 7 * 6 70 = 7 * 10 = 7 * 2 * 3 = 7 * 2 * 5
![Page 35: Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e605503460f94b5a46c/html5/thumbnails/35.jpg)
4-5 Greatest Common Factor
Examplea. Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.42 = 7 * 6 70 = 7 * 10 = 7 * 2 * 3 = 7 * 2 * 5
Then find the common factors.42 = 7 * 2 * 370 = 7 * 2 * 5
![Page 36: Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e605503460f94b5a46c/html5/thumbnails/36.jpg)
4-5 Greatest Common Factor
Examplea. Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.42 = 7 * 6 70 = 7 * 10 = 7 * 2 * 3 = 7 * 2 * 5
Then find the common factors.42 = 7 * 2 * 370 = 7 * 2 * 5
![Page 37: Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e605503460f94b5a46c/html5/thumbnails/37.jpg)
4-5 Greatest Common Factor
Examplea. Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.42 = 7 * 6 70 = 7 * 10 = 7 * 2 * 3 = 7 * 2 * 5
Then find the common factors.42 = 7 * 2 * 370 = 7 * 2 * 5
The greatest common factor of 42 and 70 is 2 * 7 or 14.
![Page 38: Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e605503460f94b5a46c/html5/thumbnails/38.jpg)
4-5 Greatest Common Factor
Exampleb. Find the greatest common factor of 6m2 and 15m
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4-5 Greatest Common Factor
Exampleb. Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m
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4-5 Greatest Common Factor
Exampleb. Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m
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4-5 Greatest Common Factor
Exampleb. Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m
Then find the common factors. 6m2 = 3 * 2 * m * m15m = 3 * 5 * m
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4-5 Greatest Common Factor
Exampleb. Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m
Then find the common factors. 6m2 = 3 * 2 * m * m15m = 3 * 5 * m
![Page 43: Factors, Primes & Composite Numbers. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e605503460f94b5a46c/html5/thumbnails/43.jpg)
4-5 Greatest Common Factor
Exampleb. Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number. 6m2 = 6 * m2 15m = 15 * m = 3 * 2 * m * m = 3 * 5 * m
Then find the common factors. 6m2 = 3 * 2 * m * m15m = 3 * 5 * m
The greatest common factor of 6m2 and 15m is 3 * m or 3m.