Question

21. By using fundamental theorem of Arithmetic show that 12" does not ends with zero.
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Answer 1

Answer:

The theorem says two things for this example: first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product.

The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, {\displaystyle 12=2\cdot 6=3\cdot 4}{\displaystyle 12=2\cdot 6=3\cdot 4}).

This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique; for example, {\displaystyle 2=2\cdot 1=2\cdot 1\cdot 1=\ldots }{\displaystyle 2=2\cdot 1=2\cdot 1\cdot 1=\ldots }

Explanation:

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Answer 2

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