It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 107, the answer is: yes, 107 is a prime number because it has only two distinct divisors: 1 and itself (107).
As a consequence, 107 is only a multiple of 1 and 107..
Since 107 is a prime number, 107 is also a deficient number, that is to say 107 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 107 without 107 itself (that is 1, by definition!).
Parity of 107
107 is an odd number, because it is not evenly divisible by 2.
Is 107 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 107 is about 10.344.
Thus, the square root of 107 is not an integer, and therefore 107 is not a square number.
Anyway, 107 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 107?
The square of a number (here 107) is the result of the product of this number (107) by itself (i.e., 107 × 107); the square of 107 is sometimes called "raising 107 to the power 2", or "107 squared".
As a consequence, 107 is the square root of 11 449.
Number of digits of 107
107 is a number with 3 digits.
What are the multiples of 107?
The multiples of 107 are all integers evenly divisible by 107, that is all numbers such that the remainder of the division by 107 is zero. There are infinitely many multiples of 107. The smallest multiples of 107 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 107 too, since 0 × 107 = 0
- 107: indeed, 107 is a multiple of itself, since 107 is evenly divisible by 107 (we have 107 / 107 = 1, so the remainder of this division is indeed zero)
- 214: indeed, 214 = 107 × 2
- 321: indeed, 321 = 107 × 3
- 428: indeed, 428 = 107 × 4
- 535: indeed, 535 = 107 × 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 107). 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 10.344). 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.