Is 104 a prime number? What are the divisors of 104?

Is 104 a prime number?

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

For 104, the answer is: No, 104 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 104) is as follows: 1, 2, 4, 8, 13, 26, 52, 104.

To be 104 a prime number, it would have been required that 104 has only two divisors, i.e., itself and 1.

As a consequence:

  • 104 is a multiple of 1
  • 104 is a multiple of 2
  • 104 is a multiple of 4
  • 104 is a multiple of 8
  • 104 is a multiple of 13
  • 104 is a multiple of 26
  • 104 is a multiple of 52

To be 104 a prime number, it would have been required that 104 has only two divisors, i.e., itself and 1.

Is 104 a deficient number?

No, 104 is not a deficient number: to be deficient, 104 should have been such that 104 is larger than the sum of its proper divisors, i.e., the divisors of 104 without 104 itself (that is 1 + 2 + 4 + 8 + 13 + 26 + 52 = 106).

In fact, 104 is an abundant number; 104 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 13 + 26 + 52 = 106). The smallest abundant number is 12.

Parity of 104

104 is an even number, because it is evenly divisible by 2: 104 / 2 = 52.

Is 104 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 104 is about 10.198.

Thus, the square root of 104 is not an integer, and therefore 104 is not a square number.

What is the square number of 104?

The square of a number (here 104) is the result of the product of this number (104) by itself (i.e., 104 × 104); the square of 104 is sometimes called "raising 104 to the power 2", or "104 squared".

The square of 104 is 10 816 because 104 × 104 = 1042 = 10 816.

As a consequence, 104 is the square root of 10 816.

Number of digits of 104

104 is a number with 3 digits.

What are the multiples of 104?

The multiples of 104 are all integers evenly divisible by 104, that is all numbers such that the remainder of the division by 104 is zero. There are infinitely many multiples of 104. The smallest multiples of 104 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 104 too, since 0 × 104 = 0
  • 104: indeed, 104 is a multiple of itself, since 104 is evenly divisible by 104 (we have 104 / 104 = 1, so the remainder of this division is indeed zero)
  • 208: indeed, 208 = 104 × 2
  • 312: indeed, 312 = 104 × 3
  • 416: indeed, 416 = 104 × 4
  • 520: indeed, 520 = 104 × 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 104). 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 10.198). 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 104

  • Preceding numbers: …102, 103
  • Following numbers: 105, 106

Nearest numbers from 104

  • Preceding prime number: 103
  • Following prime number: 107
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