Question

Find all the positive divisors of 2^ k×3​

Answer 1

Answer: 168

Step-by-step explanation:

All the positive divisors will have a prime factorization comprised of some subset of the prime factors of the number given.

You can have anything between zero to five 2  

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s in the divisor's prime factorization, that is 6 ways to take the prime factor 2, one extra for not taking 2 at all (2 raised to 0).  

Using the same logic for the other prime factors, and multiplying the number of possibilities for each:

(5+1)(6+1)(3+1)=168

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