Is 585 a prime number?

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

For 585, the answer is: No, 585 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 585) is as follows: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.

For 585 to be a prime number, it would have been required that 585 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 585 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 585 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

585 is a multiple of 1
585 is a multiple of 3
585 is a multiple of 5
585 is a multiple of 9
585 is a multiple of 13
585 is a multiple of 15
585 is a multiple of 39
585 is a multiple of 45
585 is a multiple of 65
585 is a multiple of 117
585 is a multiple of 195

For 585 to be a prime number, it would have been required that 585 has only two divisors, i.e., itself and 1.

Is 585 a deficient number?

Yes, 585 is a deficient number, that is to say 585 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 585 without 585 itself (that is 1 + 3 + 5 + 9 + 13 + 15 + 39 + 45 + 65 + 117 + 195 = 507).

Parity of 585

585 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 585 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 585 is about 24.187.

Thus, the square root of 585 is not an integer, and therefore 585 is not a square number.

What is the square number of 585?

The square of a number (here 585) is the result of the product of this number (585) by itself (i.e., 585 × 585); the square of 585 is sometimes called "raising 585 to the power 2", or "585 squared".

The square of 585 is 342 225 because 585 × 585 = 585² = 342 225.

As a consequence, 585 is the square root of 342 225.

Number of digits of 585

585 is a number with 3 digits.

What are the multiples of 585?

The multiples of 585 are all integers evenly divisible by 585, that is all numbers such that the remainder of the division by 585 is zero. There are infinitely many multiples of 585. The smallest multiples of 585 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 585 too, since 0 × 585 = 0
585: indeed, 585 is a multiple of itself, since 585 is evenly divisible by 585 (we have 585 / 585 = 1, so the remainder of this division is indeed zero)
1 170: indeed, 1 170 = 585 × 2
1 755: indeed, 1 755 = 585 × 3
2 340: indeed, 2 340 = 585 × 4
2 925: indeed, 2 925 = 585 × 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 585). 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 24.187). 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 585

Preceding numbers: …583, 584
Following numbers: 586, 587…

Nearest numbers from 585

Preceding prime number: 577
Following prime number: 587