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The only factors of a prime are 1 and itself. So, the only factor smaller than the number itself is 1. Therefore the sum of all factors smaller than the number is 1. But 1 is not a prime number.

Thus, there is no Prime number that is a perfect number.

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A polynomial of degree zero is a constant term

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Q: Why are no prime number a perfect number?
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Related questions

Can a perfect number also be a prime number and how?

A perfect number cannot be a prime.

Is one a perfect number?

no, but I don't know why. One is not a prime number and by definition of a perfect number one must be a prime number.

Can a perfect square be a prime number Explain?

No. A prime number is always odd.

Is it possible for a prime number to be a perfect number and why?

No, all prime numbers are deficient.

Is 13 a perfect number?

No, it is not.Incidentally, is a number p is prime then its 2 factors are 1 and p. Their sum is p+1.If p is a perfect number then this sum must be 2p.That is, p+1 = 2p or p = 1.But 1 is not a prime. So no prime can be a perfect number and since 13 is prime, it cannot be a perfect number.

Can a prime number be a perfect square?


Is 1 a prime number or a square number?

1 is not considered a prime number; 1 is a perfect square.

What number is a perfect square the only prime number in its prime factorization is 2 and the sum is odd?


Will the square root of a prime number be rational or irrational?

Nice question! The square root of (any number that isn't a perfect square) is irrational. No prime number is a perfect square. So the square root of any prime number is irrational.

Can a prime number be a perfect cube?

No, being a perfect cube would mean it has factors.

Why is the number 40 not a perfect square?

because it needs to be a prime number and it has to be simplified

Is there a product of two perfect squares that is not a perfect square?

No there isn't. every perfect square number can be factored into prime number. At their factoration you'll always have multiples of two on the primes exponent. Therefore you'll multiply a prime raised to a 2-multiple number with another prime raised to a 2-multiple number wich gives you also a number that factored gives you a product of prime numbers raised to a 2-multiple number and so, a perfect square.