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  • A number is said to be a nice number if it has exactly 4 factors. (Including one and number itself). Let <img alt="n=2^{3} \times 3^{2} \times 5^{3} \times 7 \times 1

A number is said to be a nice number if it has exactly 4 factors. (Including one and number itself). Let n=2^{3} \times 3^{2} \times 5^{3} \times 7 \times 11^{2}, then number of factors, which are nice numbers is

Option: 1

36


Option: 2

12


Option: 3

10


Option: 4

147


Answers (1)

best_answer

Any number having exactly 4 factors is of the form m=p^{3} (p prime) or m=p . q (where p & q are distinct primes) So we have { }^{5} \mathrm{C}_{2}+2=12 such factors.

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Divya Prakash Singh

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