Is 507 a prime number?

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

For 507, the answer is: No, 507 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 507) is as follows: 1, 3, 13, 39, 169, 507.

For 507 to be a prime number, it would have been required that 507 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

507 is a multiple of 1
507 is a multiple of 3
507 is a multiple of 13
507 is a multiple of 39
507 is a multiple of 169

For 507 to be a prime number, it would have been required that 507 has only two divisors, i.e., itself and 1.

Is 507 a deficient number?

Yes, 507 is a deficient number, that is to say 507 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 507 without 507 itself (that is 1 + 3 + 13 + 39 + 169 = 225).

Parity of 507

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

Find out more:

What is an even number?

Is 507 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 507 is about 22.517.

Thus, the square root of 507 is not an integer, and therefore 507 is not a square number.

What is the square number of 507?

The square of a number (here 507) is the result of the product of this number (507) by itself (i.e., 507 × 507); the square of 507 is sometimes called "raising 507 to the power 2", or "507 squared".

The square of 507 is 257 049 because 507 × 507 = 507² = 257 049.

As a consequence, 507 is the square root of 257 049.

Number of digits of 507

507 is a number with 3 digits.

What are the multiples of 507?

The multiples of 507 are all integers evenly divisible by 507, that is all numbers such that the remainder of the division by 507 is zero. There are infinitely many multiples of 507. The smallest multiples of 507 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 507 too, since 0 × 507 = 0
507: indeed, 507 is a multiple of itself, since 507 is evenly divisible by 507 (we have 507 / 507 = 1, so the remainder of this division is indeed zero)
1 014: indeed, 1 014 = 507 × 2
1 521: indeed, 1 521 = 507 × 3
2 028: indeed, 2 028 = 507 × 4
2 535: indeed, 2 535 = 507 × 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 507). 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 22.517). 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 507

Preceding numbers: …505, 506
Following numbers: 508, 509…

Nearest numbers from 507

Preceding prime number: 503
Following prime number: 509