Practice Fundamental Theorem Of Arithmetic (12.2.7) - Induction - Discrete Mathematics

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6 sample questions

Question 1.
What is the fundamental theorem of arithmetic?
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Think about the definition of prime numbers and how numbers can be constructed from them.
Question 2.
Provide an example of a prime number.
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Recall the definition of prime numbers.
3Question 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.
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Focus on integers greater than one.
4Question 4.
True or False: 21 can only be factored as 3 × 7.
- True
- False
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Consider if there are any other combinations for 21.
Question 5.
Prove that using a prime factorization approach, the integer 100 can come only from 2 and 5.
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Factor down all possible combinations.
Question 6.
Use the Fundamental Theorem of Arithmetic to express any number between 50 and 60 as a product of primes.
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Break down each number starting from the smallest primes.

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