What % of 2 digit natural numbers has exactly 3 factors
Answers
Answer:
if the number has 3 factors, the factors would be 1, the number itself, and a a number that could square into it... meaning that you are finding numbers that are 2-digit, postive, perfect squares with no other factors besides 1 and itself. 49 is the only number that will work
The only way to have exactly 3 factors (assuming factors positive) is to be a square of a prime. The number of factors is the product of the multiplicities of the distinct prime factors, each increased by 1. That is, for each distinct prime factor, you can make an independent choice of which power of it to include in the factor, including 0. Each such set of choices defines a unique factor, and distinct choices define different factors. As 3 is already prime, there is only one prime factor, and its multiplicity is 3- 1 = 2.
Assuming decimal representations, we need primes with squares in the range [10, 100)
(well, perhaps I don't have to assume decimal representations for that, but you know what I mean). Only 5 and 7 fit the bill; so the answer is two, namely 25 and 49