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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Total 7 numbers

numbers are: 121, 169, 289,361, 529, 841 and 961

numbers are: 121, 169, 289,361, 529, 841 and 961

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Every number has two factors - 1 and the number itself

So now the question becomes of finding a 3 digit number having exactly one factor other than 1 and the number itself.

Factors always exist in pairs which means that if x is a factor of n, then n/x is also a factor of n.

Since the number has only one factor other than 1 and the number itself, it means that x and n/x are equal, otherwise the number will have 4 factors - 1, the number itself(n), x, n/x, where x is a factor. And since the number has no other factor,x has to be a prime number.

Therefore the number is a perfect square of a prime number and is a 3 digit number - which makes 7 such numbers

So now the question becomes of finding a 3 digit number having exactly one factor other than 1 and the number itself.

Factors always exist in pairs which means that if x is a factor of n, then n/x is also a factor of n.

Since the number has only one factor other than 1 and the number itself, it means that x and n/x are equal, otherwise the number will have 4 factors - 1, the number itself(n), x, n/x, where x is a factor. And since the number has no other factor,x has to be a prime number.

Therefore the number is a perfect square of a prime number and is a 3 digit number - which makes 7 such numbers