Is 588 a prime number?

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

For 588, the answer is: No, 588 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 588) is as follows: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.

For 588 to be a prime number, it would have been required that 588 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

588 is a multiple of 1
588 is a multiple of 2
588 is a multiple of 3
588 is a multiple of 4
588 is a multiple of 6
588 is a multiple of 7
588 is a multiple of 12
588 is a multiple of 14
588 is a multiple of 21
588 is a multiple of 28
588 is a multiple of 42
588 is a multiple of 49
588 is a multiple of 84
588 is a multiple of 98
588 is a multiple of 147
588 is a multiple of 196
588 is a multiple of 294

For 588 to be a prime number, it would have been required that 588 has only two divisors, i.e., itself and 1.

Is 588 a deficient number?

No, 588 is not a deficient number: to be deficient, 588 should have been such that 588 is larger than the sum of its proper divisors, i.e., the divisors of 588 without 588 itself (that is 1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 + 49 + 84 + 98 + 147 + 196 + 294 = 1 008).

In fact, 588 is an abundant number; 588 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 7 + 12 + 14 + 21 + 28 + 42 + 49 + 84 + 98 + 147 + 196 + 294 = 1 008). The smallest abundant number is 12.

Parity of 588

588 is an even number, because it is evenly divisible by 2: 588 / 2 = 294.

Find out more:

What is an even number?

Is 588 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 588 is about 24.249.

Thus, the square root of 588 is not an integer, and therefore 588 is not a square number.

What is the square number of 588?

The square of a number (here 588) is the result of the product of this number (588) by itself (i.e., 588 × 588); the square of 588 is sometimes called "raising 588 to the power 2", or "588 squared".

The square of 588 is 345 744 because 588 × 588 = 588² = 345 744.

As a consequence, 588 is the square root of 345 744.

Number of digits of 588

588 is a number with 3 digits.

What are the multiples of 588?

The multiples of 588 are all integers evenly divisible by 588, that is all numbers such that the remainder of the division by 588 is zero. There are infinitely many multiples of 588. The smallest multiples of 588 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 588 too, since 0 × 588 = 0
588: indeed, 588 is a multiple of itself, since 588 is evenly divisible by 588 (we have 588 / 588 = 1, so the remainder of this division is indeed zero)
1 176: indeed, 1 176 = 588 × 2
1 764: indeed, 1 764 = 588 × 3
2 352: indeed, 2 352 = 588 × 4
2 940: indeed, 2 940 = 588 × 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 588). 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 24.249). 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 588

Preceding numbers: …586, 587
Following numbers: 589, 590…

Nearest numbers from 588

Preceding prime number: 587
Following prime number: 593