Is 558 a prime number? What are the divisors of 558?

Is 558 a prime number?

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

For 558, the answer is: No, 558 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 558) is as follows: 1, 2, 3, 6, 9, 18, 31, 62, 93, 186, 279, 558.

To be 558 a prime number, it would have been required that 558 has only two divisors, i.e., itself and 1.

As a consequence:

  • 558 is a multiple of 1
  • 558 is a multiple of 2
  • 558 is a multiple of 3
  • 558 is a multiple of 6
  • 558 is a multiple of 9
  • 558 is a multiple of 18
  • 558 is a multiple of 31
  • 558 is a multiple of 62
  • 558 is a multiple of 93
  • 558 is a multiple of 186
  • 558 is a multiple of 279

To be 558 a prime number, it would have been required that 558 has only two divisors, i.e., itself and 1.

Is 558 a deficient number?

No, 558 is not a deficient number: to be deficient, 558 should have been such that 558 is larger than the sum of its proper divisors, i.e., the divisors of 558 without 558 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 31 + 62 + 93 + 186 + 279 = 690).

In fact, 558 is an abundant number; 558 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 31 + 62 + 93 + 186 + 279 = 690). The smallest abundant number is 12.

Parity of 558

558 is an even number, because it is evenly divisible by 2: 558 / 2 = 279.

Is 558 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 558 is about 23.622.

Thus, the square root of 558 is not an integer, and therefore 558 is not a square number.

What is the square number of 558?

The square of a number (here 558) is the result of the product of this number (558) by itself (i.e., 558 × 558); the square of 558 is sometimes called "raising 558 to the power 2", or "558 squared".

The square of 558 is 311 364 because 558 × 558 = 5582 = 311 364.

As a consequence, 558 is the square root of 311 364.

Number of digits of 558

558 is a number with 3 digits.

What are the multiples of 558?

The multiples of 558 are all integers evenly divisible by 558, that is all numbers such that the remainder of the division by 558 is zero. There are infinitely many multiples of 558. The smallest multiples of 558 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 558 too, since 0 × 558 = 0
  • 558: indeed, 558 is a multiple of itself, since 558 is evenly divisible by 558 (we have 558 / 558 = 1, so the remainder of this division is indeed zero)
  • 1 116: indeed, 1 116 = 558 × 2
  • 1 674: indeed, 1 674 = 558 × 3
  • 2 232: indeed, 2 232 = 558 × 4
  • 2 790: indeed, 2 790 = 558 × 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 558). 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 23.622). 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 558

  • Preceding numbers: …556, 557
  • Following numbers: 559, 560

Nearest numbers from 558

  • Preceding prime number: 557
  • Following prime number: 563
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