Is 58 a prime number? What are the divisors of 58?

Is 58 a prime number?

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

For 58, the answer is: No, 58 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 58) is as follows: 1, 2, 29, 58.

To be 58 a prime number, it would have been required that 58 has only two divisors, i.e., itself and 1.

As a consequence:

  • 58 is a multiple of 1
  • 58 is a multiple of 2
  • 58 is a multiple of 29

To be 58 a prime number, it would have been required that 58 has only two divisors, i.e., itself and 1.

However, 58 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 58 = 2 x 29, where 2 and 29 are both prime numbers.

Is 58 a deficient number?

Yes, 58 is a deficient number, that is to say 58 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 58 without 58 itself (that is 1 + 2 + 29 = 32).

Parity of 58

58 is an even number, because it is evenly divisible by 2: 58 / 2 = 29.

Is 58 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 58 is about 7.616.

Thus, the square root of 58 is not an integer, and therefore 58 is not a square number.

What is the square number of 58?

The square of a number (here 58) is the result of the product of this number (58) by itself (i.e., 58 × 58); the square of 58 is sometimes called "raising 58 to the power 2", or "58 squared".

The square of 58 is 3 364 because 58 × 58 = 582 = 3 364.

As a consequence, 58 is the square root of 3 364.

Number of digits of 58

58 is a number with 2 digits.

What are the multiples of 58?

The multiples of 58 are all integers evenly divisible by 58, that is all numbers such that the remainder of the division by 58 is zero. There are infinitely many multiples of 58. The smallest multiples of 58 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 58 too, since 0 × 58 = 0
  • 58: indeed, 58 is a multiple of itself, since 58 is evenly divisible by 58 (we have 58 / 58 = 1, so the remainder of this division is indeed zero)
  • 116: indeed, 116 = 58 × 2
  • 174: indeed, 174 = 58 × 3
  • 232: indeed, 232 = 58 × 4
  • 290: indeed, 290 = 58 × 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 58). 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 7.616). 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 58

  • Preceding numbers: …56, 57
  • Following numbers: 59, 60

Nearest numbers from 58

  • Preceding prime number: 53
  • Following prime number: 59
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