Question

The number of positive integral solutions of abc=30

Answer 1

The prime factors of 30 are 2, 3, and 5.

Now let us assume the situation as 2, 3, and 5 are going to 3 places labeled as x, y, and z. All of them have to go to some of the places and more than one can go to the same place. Hence, there may be a place that does not receive any of them which is equivalent to an integer value of 1.

Hence, all of the values can go to any of the three places.
Hence, total number of integral solutions = 3*3*3 = 27

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