Beginning Activity Beginning Activity 2: Prime Factors of a Natural Number
Recall that a natural number \(p\) is a prime number provided that it is greater than 1 and the only natural numbers that divide \(p\) are 1 and \(p\text{.}\) A natural number other than 1 that is not a prime number is a composite number. The number 1 is neither prime nor composite.
1.
Give examples of four natural numbers that are prime and four natural numbers that are composite.
2.
Write each of the natural numbers 20, 40, 50, and 150 as a product of prime numbers.
3.
Do you think that any composite number can be written as a product of prime numbers?
4.
Write a useful description of what it means to say that a natural number is a composite number (other than saying that it is not prime).
5.
Based on your work in Exercise 2, do you think it would be possible to use induction to prove that any composite number can be written as a product of prime numbers?