Is 821567563 a prime number?
It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 821 567 563 is a prime number.
Indeed, the definition of a prime numbers is to have exactly two distinct positive divisors, 1 and itself. A number is a divisor of another number when the remainder of Euclid’s division of the second one by the first one is zero. Concerning the number 821 567 563, the only two divisors are 1 and 821 567 563. Therefore 821 567 563 is a prime number.
As a consequence, 821 567 563 is only a multiple of 1 and 821 567 563.
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Since 821567563 is a prime number, 821567563 is also a deficient number, that is to say 821567563 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 821567563 without 821567563 itself (that is 1, by definition!).