It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 877, the answer is: yes, 877 is a prime number because it has only two distinct divisors: 1 and itself (877).
As a consequence, 877 is only a multiple of 1 and 877..
Since 877 is a prime number, 877 is also a deficient number, that is to say 877 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 877 without 877 itself (that is 1, by definition!).
Parity of 877
877 is an odd number, because it is not evenly divisible by 2.
Is 877 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 877 is about 29.614.
Thus, the square root of 877 is not an integer, and therefore 877 is not a square number.
Anyway, 877 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 877?
The square of a number (here 877) is the result of the product of this number (877) by itself (i.e., 877 × 877); the square of 877 is sometimes called "raising 877 to the power 2", or "877 squared".
As a consequence, 877 is the square root of 769 129.
Number of digits of 877
877 is a number with 3 digits.
What are the multiples of 877?
The multiples of 877 are all integers evenly divisible by 877, that is all numbers such that the remainder of the division by 877 is zero. There are infinitely many multiples of 877. The smallest multiples of 877 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 877 too, since 0 × 877 = 0
- 877: indeed, 877 is a multiple of itself, since 877 is evenly divisible by 877 (we have 877 / 877 = 1, so the remainder of this division is indeed zero)
- 1 754: indeed, 1 754 = 877 × 2
- 2 631: indeed, 2 631 = 877 × 3
- 3 508: indeed, 3 508 = 877 × 4
- 4 385: indeed, 4 385 = 877 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 877). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 29.614). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.