It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 131, the answer is: yes, 131 is a prime number because it has only two distinct divisors: 1 and itself (131).
As a consequence, 131 is only a multiple of 1 and 131..
Since 131 is a prime number, 131 is also a deficient number, that is to say 131 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 131 without 131 itself (that is 1, by definition!).
Parity of 131
131 is an odd number, because it is not evenly divisible by 2.
Is 131 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 131 is about 11.446.
Thus, the square root of 131 is not an integer, and therefore 131 is not a square number.
Anyway, 131 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 131?
The square of a number (here 131) is the result of the product of this number (131) by itself (i.e., 131 × 131); the square of 131 is sometimes called "raising 131 to the power 2", or "131 squared".
As a consequence, 131 is the square root of 17 161.
Number of digits of 131
131 is a number with 3 digits.
What are the multiples of 131?
The multiples of 131 are all integers evenly divisible by 131, that is all numbers such that the remainder of the division by 131 is zero. There are infinitely many multiples of 131. The smallest multiples of 131 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 131 too, since 0 × 131 = 0
- 131: indeed, 131 is a multiple of itself, since 131 is evenly divisible by 131 (we have 131 / 131 = 1, so the remainder of this division is indeed zero)
- 262: indeed, 262 = 131 × 2
- 393: indeed, 393 = 131 × 3
- 524: indeed, 524 = 131 × 4
- 655: indeed, 655 = 131 × 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 131). 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 11.446). 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.