It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 907, the answer is: yes, 907 is a prime number because it has only two distinct divisors: 1 and itself (907).
As a consequence, 907 is only a multiple of 1 and 907..
Since 907 is a prime number, 907 is also a deficient number, that is to say 907 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 907 without 907 itself (that is 1, by definition!).
Parity of 907
907 is an odd number, because it is not evenly divisible by 2.
Is 907 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 907 is about 30.116.
Thus, the square root of 907 is not an integer, and therefore 907 is not a square number.
Anyway, 907 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 907?
The square of a number (here 907) is the result of the product of this number (907) by itself (i.e., 907 × 907); the square of 907 is sometimes called "raising 907 to the power 2", or "907 squared".
As a consequence, 907 is the square root of 822 649.
Number of digits of 907
907 is a number with 3 digits.
What are the multiples of 907?
The multiples of 907 are all integers evenly divisible by 907, that is all numbers such that the remainder of the division by 907 is zero. There are infinitely many multiples of 907. The smallest multiples of 907 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 907 too, since 0 × 907 = 0
- 907: indeed, 907 is a multiple of itself, since 907 is evenly divisible by 907 (we have 907 / 907 = 1, so the remainder of this division is indeed zero)
- 1 814: indeed, 1 814 = 907 × 2
- 2 721: indeed, 2 721 = 907 × 3
- 3 628: indeed, 3 628 = 907 × 4
- 4 535: indeed, 4 535 = 907 × 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 907). 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 30.116). 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.