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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.