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Math 50

Math 50. 3.5 – Prime Numbers and GCF. A natural number that has exactly two different factors (1 and itself) is called a __________________ . A natural number that has factors other than 1 and itself is called a _________________________ .

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Math 50

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  1. Math 50 3.5 – Prime Numbers and GCF

  2. A natural number that has exactly two different factors (1 and itself) is called a __________________. A natural number that has factors other than 1 and itself is called a _________________________.

  3. A natural number that has exactly two different factors (1 and itself) is called a __________________. A natural number that has factors other than 1 and itself is called a _________________________. prime number

  4. A natural number that has exactly two different factors (1 and itself) is called a __________________. A natural number that has factors other than 1 and itself is called a _________________________. prime number composite number

  5. Here’s a short list of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, …

  6. Notes: ___ is the only natural # that is neither prime nor composite. Natural numbers bigger than 1 are either prime or composite, but not both.

  7. Notes: ___ is the only natural # that is neither prime nor composite. Natural numbers bigger than 1 are either prime or composite, but not both. 1

  8. Notes: ___ is the only natural # that is neither prime nor composite. Natural numbers bigger than 1 are either prime or composite, but not both. 1

  9. Is a # prime? 1. ___________ # by larger and larger ___________ (2, 3, 5, 7, …) 2. If # is divisible by a prime, then # is composite. 3. If not, continue dividing by primes until _________________________, at which point you can stop and call your # a prime.

  10. Is a # prime? 1. ___________ # by larger and larger ___________ (2, 3, 5, 7, …) 2. If # is divisible by a prime, then # is composite. 3. If not, continue dividing by primes until _________________________, at which point you can stop and call your # a prime. Divide

  11. Is a # prime? 1. ___________ # by larger and larger ___________ (2, 3, 5, 7, …) 2. If # is divisible by a prime, then # is composite. 3. If not, continue dividing by primes until _________________________, at which point you can stop and call your # a prime. Divide primes

  12. Is a # prime? 1. ___________ # by larger and larger ___________ (2, 3, 5, 7, …) 2. If # is divisible by a prime, then # is composite. 3. If not, continue dividing by primes until _________________________, at which point you can stop and call your # a prime. Divide primes quotient divisor

  13. Ex 1.Is 119 prime or composite? Ex 2.Is 157 prime or composite?

  14. A product written with prime factors onlyis called a ______________________________. We can write the prime factorization for any composite number. For example, the prime factorization of is , or using exponential form . We’ll use “factor trees” to help find prime factorization of numbers.

  15. A product written with prime factors onlyis called a ______________________________. We can write the prime factorization for any composite number. For example, the prime factorization of is , or using exponential form . We’ll use “factor trees” to help find prime factorization of numbers. prime factorization

  16. A product written with prime factors onlyis called a ______________________________. We can write the prime factorization for any composite number. For example, the prime factorization of is , or using exponential form . We’ll use “factor trees” to help find prime factorization of numbers. prime factorization

  17. A product written with prime factors onlyis called a ______________________________. We can write the prime factorization for any composite number. For example, the prime factorization of is , or using exponential form . We’ll use “factor trees” to help find prime factorization of numbers. prime factorization

  18. Ex 3.Use a factor tree to find the prime factorization of . Write the answer in exponential form.

  19. To list all factors of a number, ___________ by ____________________ until you have all the factors. Ex 4.List all factors of 60.

  20. To list all factors of a number, ___________ by ____________________ until you have all the factors. Ex 4.List all factors of 60. divide

  21. To list all factors of a number, ___________ by ____________________ until you have all the factors. Ex 4.List all factors of 60. divide natural numbers

  22. To list all factors of a number, ___________ by ____________________ until you have all the factors. Ex 4.List all factors of 60. divide natural numbers

  23. The greatest number that divides all given numbers with no remainder is called the ____________________________________. ex: The GCF of 32, 40, and 24 is 8. Why? Since 32, 40, and 24 are divisible by 8, and 8 is the greatest such number.

  24. The greatest number that divides all given numbers with no remainder is called the ____________________________________. ex: The GCF of 32, 40, and 24 is 8. Why? Since 32, 40, and 24 are divisible by 8, and 8 is the greatest such number. greatest common factor (GCF)

  25. The greatest number that divides all given numbers with no remainder is called the ____________________________________. ex: The GCF of 32, 40, and 24 is 8. Why? Since 32, 40, and 24 are divisible by 8, and 8 is the greatest such number. greatest common factor (GCF)

  26. Ex 5.Find the GCF of 36 and 54 by listing factors.

  27. How to find GCF using prime factorization 1. Write __________________________ of each # in exponential form. 2. Make factorization that contains prime #’s common to all above factorizations, each raised to least of its exponents. 3. Multiply to get GCF. (Note: if no common prime factors, then GCF is 1)

  28. How to find GCF using prime factorization 1. Write __________________________ of each # in exponential form. 2. Make factorization that contains prime #’s common to all above factorizations, each raised to least of its exponents. 3. Multiply to get GCF. (Note: if no common prime factors, then GCF is 1) prime factorization

  29. How to find GCF using prime factorization 1. Write __________________________ of each # in exponential form. 2. Make factorization that contains prime #’s common to all above factorizations, each raised to least of its exponents. 3. Multiply to get GCF. (Note: if no common prime factors, then GCF is 1) prime factorization

  30. Ex 6.Find the GCF of 84 and 48 using prime factorization. Ex 7.Find the GCF of 60 and 77 using prime factorization.

  31. Ex 8.A rectangular kitchen floor measures 18 feet long by 16 feet wide. What is the largest-size square tile that can be used to cover the floor without cutting or overlapping the tiles?

  32. GCF of Monomials Ex 9.Find the GCF of and . Ex 10.Find the GCF of , , and .

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