Is 504 a prime number?

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

For 504, the answer is: No, 504 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 504) is as follows: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.

For 504 to be a prime number, it would have been required that 504 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

504 is a multiple of 1
504 is a multiple of 2
504 is a multiple of 3
504 is a multiple of 4
504 is a multiple of 6
504 is a multiple of 7
504 is a multiple of 8
504 is a multiple of 9
504 is a multiple of 12
504 is a multiple of 14
504 is a multiple of 18
504 is a multiple of 21
504 is a multiple of 24
504 is a multiple of 28
504 is a multiple of 36
504 is a multiple of 42
504 is a multiple of 56
504 is a multiple of 63
504 is a multiple of 72
504 is a multiple of 84
504 is a multiple of 126
504 is a multiple of 168
504 is a multiple of 252

For 504 to be a prime number, it would have been required that 504 has only two divisors, i.e., itself and 1.

Is 504 a deficient number?

No, 504 is not a deficient number: to be deficient, 504 should have been such that 504 is larger than the sum of its proper divisors, i.e., the divisors of 504 without 504 itself (that is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 28 + 36 + 42 + 56 + 63 + 72 + 84 + 126 + 168 + 252 = 1 056).

In fact, 504 is an abundant number; 504 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 + 12 + 14 + 18 + 21 + 24 + 28 + 36 + 42 + 56 + 63 + 72 + 84 + 126 + 168 + 252 = 1 056). The smallest abundant number is 12.

Parity of 504

504 is an even number, because it is evenly divisible by 2: 504 / 2 = 252.

Find out more:

What is an even number?

Is 504 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 504 is about 22.450.

Thus, the square root of 504 is not an integer, and therefore 504 is not a square number.

What is the square number of 504?

The square of a number (here 504) is the result of the product of this number (504) by itself (i.e., 504 × 504); the square of 504 is sometimes called "raising 504 to the power 2", or "504 squared".

The square of 504 is 254 016 because 504 × 504 = 504² = 254 016.

As a consequence, 504 is the square root of 254 016.

Number of digits of 504

504 is a number with 3 digits.

What are the multiples of 504?

The multiples of 504 are all integers evenly divisible by 504, that is all numbers such that the remainder of the division by 504 is zero. There are infinitely many multiples of 504. The smallest multiples of 504 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 504 too, since 0 × 504 = 0
504: indeed, 504 is a multiple of itself, since 504 is evenly divisible by 504 (we have 504 / 504 = 1, so the remainder of this division is indeed zero)
1 008: indeed, 1 008 = 504 × 2
1 512: indeed, 1 512 = 504 × 3
2 016: indeed, 2 016 = 504 × 4
2 520: indeed, 2 520 = 504 × 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 504). 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 22.450). 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 504

Preceding numbers: …502, 503
Following numbers: 505, 506…

Nearest numbers from 504

Preceding prime number: 503
Following prime number: 509