It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 641, the answer is: yes, 641 is a prime number because it has only two distinct divisors: 1 and itself (641).
As a consequence, 641 is only a multiple of 1 and 641..
Since 641 is a prime number, 641 is also a deficient number, that is to say 641 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 641 without 641 itself (that is 1, by definition!).
Parity of 641
641 is an odd number, because it is not evenly divisible by 2.
Is 641 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 641 is about 25.318.
Thus, the square root of 641 is not an integer, and therefore 641 is not a square number.
Anyway, 641 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 641?
The square of a number (here 641) is the result of the product of this number (641) by itself (i.e., 641 × 641); the square of 641 is sometimes called "raising 641 to the power 2", or "641 squared".
As a consequence, 641 is the square root of 410 881.
Number of digits of 641
641 is a number with 3 digits.
What are the multiples of 641?
The multiples of 641 are all integers evenly divisible by 641, that is all numbers such that the remainder of the division by 641 is zero. There are infinitely many multiples of 641. The smallest multiples of 641 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 641 too, since 0 × 641 = 0
- 641: indeed, 641 is a multiple of itself, since 641 is evenly divisible by 641 (we have 641 / 641 = 1, so the remainder of this division is indeed zero)
- 1 282: indeed, 1 282 = 641 × 2
- 1 923: indeed, 1 923 = 641 × 3
- 2 564: indeed, 2 564 = 641 × 4
- 3 205: indeed, 3 205 = 641 × 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 641). 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 25.318). 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.