Is 500 a prime number?

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

For 500, the answer is: No, 500 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 500) is as follows: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500.

For 500 to be a prime number, it would have been required that 500 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 500 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 500 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

500 is a multiple of 1
500 is a multiple of 2
500 is a multiple of 4
500 is a multiple of 5
500 is a multiple of 10
500 is a multiple of 20
500 is a multiple of 25
500 is a multiple of 50
500 is a multiple of 100
500 is a multiple of 125
500 is a multiple of 250

For 500 to be a prime number, it would have been required that 500 has only two divisors, i.e., itself and 1.

Is 500 a deficient number?

No, 500 is not a deficient number: to be deficient, 500 should have been such that 500 is larger than the sum of its proper divisors, i.e., the divisors of 500 without 500 itself (that is 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 + 125 + 250 = 592).

In fact, 500 is an abundant number; 500 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 + 125 + 250 = 592). The smallest abundant number is 12.

Parity of 500

500 is an even number, because it is evenly divisible by 2: 500 / 2 = 250.

Find out more:

What is an even number?

Is 500 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 500 is about 22.361.

Thus, the square root of 500 is not an integer, and therefore 500 is not a square number.

What is the square number of 500?

The square of a number (here 500) is the result of the product of this number (500) by itself (i.e., 500 × 500); the square of 500 is sometimes called "raising 500 to the power 2", or "500 squared".

The square of 500 is 250 000 because 500 × 500 = 500² = 250 000.

As a consequence, 500 is the square root of 250 000.

Number of digits of 500

500 is a number with 3 digits.

What are the multiples of 500?

The multiples of 500 are all integers evenly divisible by 500, that is all numbers such that the remainder of the division by 500 is zero. There are infinitely many multiples of 500. The smallest multiples of 500 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 500 too, since 0 × 500 = 0
500: indeed, 500 is a multiple of itself, since 500 is evenly divisible by 500 (we have 500 / 500 = 1, so the remainder of this division is indeed zero)
1 000: indeed, 1 000 = 500 × 2
1 500: indeed, 1 500 = 500 × 3
2 000: indeed, 2 000 = 500 × 4
2 500: indeed, 2 500 = 500 × 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 500). 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 22.361). 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 500

Preceding numbers: …498, 499
Following numbers: 501, 502…

Nearest numbers from 500

Preceding prime number: 499
Following prime number: 503