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A perfect number is a positive integer whose factors (excluding the number itself) add up the number; 6 is a perfect number:
1 x 2 x 3 = 6
1 + 2 + 3 = 6
Prime numbers, by definition, don't have factors, so cannot be perfect. In fact, it may be that odd numbers can't be perfect.
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Is it possible for a prime number to be a perfect number and why?
No, all prime numbers are deficient.
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.
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 perfect square be a prime number Explain?
No. A prime number is always odd.
Can a prime number be a perfect square?
No.
Is it possible for a multiple of 13 greater then 13 to be a prime number?
It is not possible for any multiple of a prime number to be prime.
Is 1 a prime number or a square number?
1 is not considered a prime number; 1 is a perfect square.
Why are no prime number a perfect number?
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.
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.
What number is a perfect square the only prime number in its prime factorization is 2 and the sum is odd?
16
Is it possible for 53 to be prime?
53 is a prime number.
