It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 977, the answer is: yes, 977 is a prime number because it has only two distinct divisors: 1 and itself (977).
As a consequence, 977 is only a multiple of 1 and 977..
Since 977 is a prime number, 977 is also a deficient number, that is to say 977 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 977 without 977 itself (that is 1, by definition!).
Parity of 977
977 is an odd number, because it is not evenly divisible by 2.
Is 977 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 977 is about 31.257.
Thus, the square root of 977 is not an integer, and therefore 977 is not a square number.
Anyway, 977 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 977?
The square of a number (here 977) is the result of the product of this number (977) by itself (i.e., 977 × 977); the square of 977 is sometimes called "raising 977 to the power 2", or "977 squared".
As a consequence, 977 is the square root of 954 529.
Number of digits of 977
977 is a number with 3 digits.
What are the multiples of 977?
The multiples of 977 are all integers evenly divisible by 977, that is all numbers such that the remainder of the division by 977 is zero. There are infinitely many multiples of 977. The smallest multiples of 977 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 977 too, since 0 × 977 = 0
- 977: indeed, 977 is a multiple of itself, since 977 is evenly divisible by 977 (we have 977 / 977 = 1, so the remainder of this division is indeed zero)
- 1 954: indeed, 1 954 = 977 × 2
- 2 931: indeed, 2 931 = 977 × 3
- 3 908: indeed, 3 908 = 977 × 4
- 4 885: indeed, 4 885 = 977 × 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 977). 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 31.257). 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.