factors

Question

how many numbers less than 1000 will have exactly 3 factor?

Answer 1

Let's say N have 3 factors.

1 and N will always be its 2 factors. So only 1 factor is left.

Now we need to take number P having only 1 factor > 1 and < P.

This number P can only be (prime)².

So total squares of prime < 1000.

eg.

4 = 2² = Factors(1, 2, 4)

9 = 3² = Factors(1, 3, 9)

25 = 5² = Factors(1, 5, 25)

49 = 7² = Factors(1, 7, 49)

...

961 = 31² = Factors(1, 31, 961)

Till 31² are < 1000.

N = (2², 3², 5², 7², 9², 11², 13², 17², 19², 23², 29², 31²)

Total numbers < 1000 with exactly 3 factors = 12

Comments

really v nice explanation

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total number  <1000 with exactly 3 factors =11 bcoz 9 is not a prime number.

9^2 =81

81 has 5 factors 1,3,9,37,81