Every natural number is the product of primes. (Treat 1 as an empty product.) So

Question

Explanation / Answer

Treating one as an empty product, we focus on any natural number greater than or equal to 2. For each number n in N>= 2: Case 1: n is prime. We are done. Case 2: n is not prime. Step 1- By definition, we can find two natural numbers j, k, such that j*k=n, where j and k both are not equal to 1. Step 2- We then test j and k. If they are prime, then we are done, for each factor j or k that is not prime, return to step 1 and continue factoring. By definition, any time we have a non-prime number in our product, we can further factor it using step 1 iteratively until we have a product of prime numbers.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.