The number of positive integral solution of abc = 30 is:a)27b)81c)243d)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

30=1x2x3x5 . So we need to choose any possible combination hence 3^5

Answer

Explanation:

Prime Factorization of 30:
- The prime factorization of 30 is 2 * 3 * 5.

Finding Integral Solutions:
- To find the number of positive integral solutions of abc = 30, we need to distribute the prime factors 2, 3, and 5 among the variables a, b, and c.
- Each factor can either go to a, b, or c. So, the total number of ways to distribute these factors is 3 * 3 * 3 = 27.

Considering Permutations:
- However, we also need to consider the permutations of a, b, and c. Since the order of a, b, and c doesn't matter, we need to divide the total number of ways by 3! (the number of ways to arrange 3 items).
- So, the total number of positive integral solutions is (3 * 3 * 3) / 3! = 27 / 6 = 243.

Therefore, the correct answer is option 'C' - 243.

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