12.2.7. Fundamental Theorem of Arithmetic

Try these first

1. 1.

   What is the fundamental theorem of arithmetic?

   Hint

   Think about the definition of prime numbers and how numbers can be constructed from them.

2. 2.

   Provide an example of a prime number.

   Hint

   Recall the definition of prime numbers.

3. 3.

   What does the Fundamental Theorem of Arithmetic state?

   • Every integer can be expressed in multiple ways.
   • Every integer greater than 1 can be expressed as a product of prime numbers.
   • Only prime numbers have unique factors.

   Hint

   Focus on integers greater than one.

4. 4.

   True or False: 21 can only be factored as 3 × 7.

   • True
   • False

   Hint

   Consider if there are any other combinations for 21.

5. 5.

   Prove that using a prime factorization approach, the integer 100 can come only from 2 and 5.

   Hint

   Factor down all possible combinations.

6. 6.

   Use the Fundamental Theorem of Arithmetic to express any number between 50 and 60 as a product of primes.

   Hint

   Break down each number starting from the smallest primes.