Question

The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 12 positive factors, including 1 and k

Answer 1

Answer:

k = 63

Step-by-step explanation:

Given: k's factors are 1, 3, 7, ___, ___, and k. (1) is a factor of k. This implies that there are two factors of 3 i..e, 9 is also a factor of k. Also, is a factor of k. Therefore, k's factors are 1, 3, 7, 9, 21, and k. As there are two 3's and a 7 in factors of k, then is also a factor. (2) is not a factor of K. If is not a factor of k and total number of factors is 6, there must be two factors of 3 ('K' has exactly two positive prime factors) as otherwise, if we use a non-prime factor, then k would have more than 6 factors. So, K's factors are 1, 3, 7, 9, 21, 63.

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