9
Question
The number of positive integral solutions of abc=30 is
The number of positive integral solutions of abc=30 is
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Solution
The correct option is B 27
30 = 2 × 3 × 5
These are exactly 3 prime
factors, and the first solution
If we consider 1 to
be a factor we have more solutions:
30 = 1 × 2 × 3 × 5 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 = 1 × 2 × 15
30 = 1 × 3 × 10
30 = 1 × 5 × 6
And we have the very obvious:
30 = 1 × 1 × 30
For a total of 5 solutions
The first four solutions can be done in six orders each, and the
fifth solution can be done in three orders.
Total 27
30 = 2 × 3 × 5
These are exactly 3 prime
factors, and the first solution
If we consider 1 to
be a factor we have more solutions:
30 = 1 × 2 × 3 × 5 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 = 1 × 2 × 15
30 = 1 × 3 × 10
30 = 1 × 5 × 6
And we have the very obvious:
30 = 1 × 1 × 30
For a total of 5 solutions
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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