It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 677, the answer is: yes, 677 is a prime number because it has only two distinct divisors: 1 and itself (677).
As a consequence, 677 is only a multiple of 1 and 677..
Since 677 is a prime number, 677 is also a deficient number, that is to say 677 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 677 without 677 itself (that is 1, by definition!).
Parity of 677
677 is an odd number, because it is not evenly divisible by 2.
Is 677 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 677 is about 26.019.
Thus, the square root of 677 is not an integer, and therefore 677 is not a square number.
Anyway, 677 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 677?
The square of a number (here 677) is the result of the product of this number (677) by itself (i.e., 677 × 677); the square of 677 is sometimes called "raising 677 to the power 2", or "677 squared".
As a consequence, 677 is the square root of 458 329.
Number of digits of 677
677 is a number with 3 digits.
What are the multiples of 677?
The multiples of 677 are all integers evenly divisible by 677, that is all numbers such that the remainder of the division by 677 is zero. There are infinitely many multiples of 677. The smallest multiples of 677 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 677 too, since 0 × 677 = 0
- 677: indeed, 677 is a multiple of itself, since 677 is evenly divisible by 677 (we have 677 / 677 = 1, so the remainder of this division is indeed zero)
- 1 354: indeed, 1 354 = 677 × 2
- 2 031: indeed, 2 031 = 677 × 3
- 2 708: indeed, 2 708 = 677 × 4
- 3 385: indeed, 3 385 = 677 × 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 677). 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 26.019). 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.