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A Quickie (Posted on 2015-03-13)

How many 3-digit integers have exactly 7 divisors?

No Solution Yet Submitted by Ady TZIDON

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solution Comment 1 of 1

just one. 3^6=729.

The number of divisors can be computed by looking at the prime factorization
(p1^a1)(p2^a2)...
and is given by the product
(a1+1)(a2+1)...

Since 7 is prime, the only product is
(a1+1)=7
a1 = 6

So only number if the form p^6 have 7 divisors.
And only 3^6 is a 3 digit number.

Posted by Jer on 2015-03-13 08:50:08

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