Is 108 a prime number? What are the divisors of 108?

Is 108 a prime number?

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

For 108, the answer is: No, 108 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 108) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.

To be 108 a prime number, it would have been required that 108 has only two divisors, i.e., itself and 1.

As a consequence:

  • 108 is a multiple of 1
  • 108 is a multiple of 2
  • 108 is a multiple of 3
  • 108 is a multiple of 4
  • 108 is a multiple of 6
  • 108 is a multiple of 9
  • 108 is a multiple of 12
  • 108 is a multiple of 18
  • 108 is a multiple of 27
  • 108 is a multiple of 36
  • 108 is a multiple of 54

To be 108 a prime number, it would have been required that 108 has only two divisors, i.e., itself and 1.

Is 108 a deficient number?

No, 108 is not a deficient number: to be deficient, 108 should have been such that 108 is larger than the sum of its proper divisors, i.e., the divisors of 108 without 108 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 = 172).

In fact, 108 is an abundant number; 108 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 = 172). The smallest abundant number is 12.

Parity of 108

108 is an even number, because it is evenly divisible by 2: 108 / 2 = 54.

Is 108 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 108 is about 10.392.

Thus, the square root of 108 is not an integer, and therefore 108 is not a square number.

What is the square number of 108?

The square of a number (here 108) is the result of the product of this number (108) by itself (i.e., 108 × 108); the square of 108 is sometimes called "raising 108 to the power 2", or "108 squared".

The square of 108 is 11 664 because 108 × 108 = 1082 = 11 664.

As a consequence, 108 is the square root of 11 664.

Number of digits of 108

108 is a number with 3 digits.

What are the multiples of 108?

The multiples of 108 are all integers evenly divisible by 108, that is all numbers such that the remainder of the division by 108 is zero. There are infinitely many multiples of 108. The smallest multiples of 108 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 108 too, since 0 × 108 = 0
  • 108: indeed, 108 is a multiple of itself, since 108 is evenly divisible by 108 (we have 108 / 108 = 1, so the remainder of this division is indeed zero)
  • 216: indeed, 216 = 108 × 2
  • 324: indeed, 324 = 108 × 3
  • 432: indeed, 432 = 108 × 4
  • 540: indeed, 540 = 108 × 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 108). 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 10.392). 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 108

  • Preceding numbers: …106, 107
  • Following numbers: 109, 110

Nearest numbers from 108

  • Preceding prime number: 107
  • Following prime number: 109
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