The number of positive integral solutions of ABC =30 is?

1 Answer
MeneerNask
Jul 3, 2018

We first factorize #30# into primes.

Explanation:

#30=2xx3xx5#
These are exactly #3# prime factors, and the first solution

If we consider #1# to be a factor we have more solutions:
#30=1xx2xx3xx5# and we can take one of the primes to be the second factor, and the product of the other two to be the third:

#30=1xx2xx15#
#30=1xx3xx10#
#30=1xx5xx6#

And we have the very obvious:
#30=1xx1xx30#

For a total of #5# solutions

If the order of A, B and C is important (that is if #2,3,5# is different from #2,5,3#) then there are more solutions still:

The first four solutions can be done in six orders each, and the fifth solution can be done in three orders.

Total #27#

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