It is possible to find out using mathematical methods whether a given integer is a prime number or not.
Yes, 110 880 877 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 110 880 877, the only two divisors are 1 and 110 880 877. Therefore 110 880 877 is a prime number.
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Since 110880877 is a prime number, 110880877 is also a deficient number, that is to say 110880877 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 110880877 without 110880877 itself (that is 1, by definition!).