It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 631, the answer is: yes, 631 is a prime number because it has only two distinct divisors: 1 and itself (631).
As a consequence, 631 is only a multiple of 1 and 631..
Since 631 is a prime number, 631 is also a deficient number, that is to say 631 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 631 without 631 itself (that is 1, by definition!).
Parity of 631
631 is an odd number, because it is not evenly divisible by 2.
Is 631 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 631 is about 25.120.
Thus, the square root of 631 is not an integer, and therefore 631 is not a square number.
Anyway, 631 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 631?
The square of a number (here 631) is the result of the product of this number (631) by itself (i.e., 631 × 631); the square of 631 is sometimes called "raising 631 to the power 2", or "631 squared".
As a consequence, 631 is the square root of 398 161.
Number of digits of 631
631 is a number with 3 digits.
What are the multiples of 631?
The multiples of 631 are all integers evenly divisible by 631, that is all numbers such that the remainder of the division by 631 is zero. There are infinitely many multiples of 631. The smallest multiples of 631 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 631 too, since 0 × 631 = 0
- 631: indeed, 631 is a multiple of itself, since 631 is evenly divisible by 631 (we have 631 / 631 = 1, so the remainder of this division is indeed zero)
- 1 262: indeed, 1 262 = 631 × 2
- 1 893: indeed, 1 893 = 631 × 3
- 2 524: indeed, 2 524 = 631 × 4
- 3 155: indeed, 3 155 = 631 × 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 631). 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 25.120). 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.