Prime Numbers and Composite Numbers 5-4
A prime number is a positive integer greater than 1 with exactly two factors, 1 and the number itself. The numbers 2, 3, 5, 7 are examples of prime numbers
A composite number is a positive integer greater than 1 with more than two factors. The numbers 4, 6, 8, 9, and 10 are examples of composite numbers.
Since 1 has exactly 1 factor, it is neither prime nor composite.
About 230 BCE Erathosthenes, a Greek Mathematician suggested a way to find prime numbers—up to a specific number. The method is called the Sieve of Eratosthenes because it picks out the prime numbers as a strainer, or sieve, picks out solid particles from a liquid.
You may factor a number into prime factors by using either of the following methods
➢ Inverted short division
➢ Factor tree
Both were shown in class.
Could you start the factor tree differently? If so, would you end up with the same answer?
The prime factors of 42 are the same in either factor tree, except for their order.
Every composite number greater than 1 can be written as a product of prime factors in exactly one way, except for the order of the factors.
When we write 42 as 2 ∙ 3 ∙ 7 this product is called the prime factorization of 42
Notice the order in which prime factorization is written.
Let’s try finding the prime factorization of 60
The prime factorization of 60 = 2 ∙ 2∙ 3 ∙ 5 or 22∙ 3∙ 5
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