Is 115 a prime number? What are the divisors of 115?

Is 115 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 115, the answer is: No, 115 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 115) is as follows: 1, 5, 23, 115.

To be 115 a prime number, it would have been required that 115 has only two divisors, i.e., itself and 1.

As a consequence:

  • 115 is a multiple of 1
  • 115 is a multiple of 5
  • 115 is a multiple of 23

To be 115 a prime number, it would have been required that 115 has only two divisors, i.e., itself and 1.

However, 115 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 115 = 5 x 23, where 5 and 23 are both prime numbers.

Is 115 a deficient number?

Yes, 115 is a deficient number, that is to say 115 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 115 without 115 itself (that is 1 + 5 + 23 = 29).

Parity of 115

115 is an odd number, because it is not evenly divisible by 2.

Is 115 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 115 is about 10.724.

Thus, the square root of 115 is not an integer, and therefore 115 is not a square number.

What is the square number of 115?

The square of a number (here 115) is the result of the product of this number (115) by itself (i.e., 115 × 115); the square of 115 is sometimes called "raising 115 to the power 2", or "115 squared".

The square of 115 is 13 225 because 115 × 115 = 1152 = 13 225.

As a consequence, 115 is the square root of 13 225.

Number of digits of 115

115 is a number with 3 digits.

What are the multiples of 115?

The multiples of 115 are all integers evenly divisible by 115, that is all numbers such that the remainder of the division by 115 is zero. There are infinitely many multiples of 115. The smallest multiples of 115 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 115 too, since 0 × 115 = 0
  • 115: indeed, 115 is a multiple of itself, since 115 is evenly divisible by 115 (we have 115 / 115 = 1, so the remainder of this division is indeed zero)
  • 230: indeed, 230 = 115 × 2
  • 345: indeed, 345 = 115 × 3
  • 460: indeed, 460 = 115 × 4
  • 575: indeed, 575 = 115 × 5
  • etc.

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 115). 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 10.724). 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.

Numbers near 115

  • Preceding numbers: …113, 114
  • Following numbers: 116, 117

Nearest numbers from 115

  • Preceding prime number: 113
  • Following prime number: 127
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