Is 501 a prime number?

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

For 501, the answer is: No, 501 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 501) is as follows: 1, 3, 167, 501.

For 501 to be a prime number, it would have been required that 501 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

501 is a multiple of 1
501 is a multiple of 3
501 is a multiple of 167

For 501 to be a prime number, it would have been required that 501 has only two divisors, i.e., itself and 1.

However, 501 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 501 = 3 x 167, where 3 and 167 are both prime numbers.

Is 501 a deficient number?

Yes, 501 is a deficient number, that is to say 501 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 501 without 501 itself (that is 1 + 3 + 167 = 171).

Parity of 501

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

Find out more:

What is an even number?

Is 501 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 501 is about 22.383.

Thus, the square root of 501 is not an integer, and therefore 501 is not a square number.

What is the square number of 501?

The square of a number (here 501) is the result of the product of this number (501) by itself (i.e., 501 × 501); the square of 501 is sometimes called "raising 501 to the power 2", or "501 squared".

The square of 501 is 251 001 because 501 × 501 = 501² = 251 001.

As a consequence, 501 is the square root of 251 001.

Number of digits of 501

501 is a number with 3 digits.

What are the multiples of 501?

The multiples of 501 are all integers evenly divisible by 501, that is all numbers such that the remainder of the division by 501 is zero. There are infinitely many multiples of 501. The smallest multiples of 501 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 501 too, since 0 × 501 = 0
501: indeed, 501 is a multiple of itself, since 501 is evenly divisible by 501 (we have 501 / 501 = 1, so the remainder of this division is indeed zero)
1 002: indeed, 1 002 = 501 × 2
1 503: indeed, 1 503 = 501 × 3
2 004: indeed, 2 004 = 501 × 4
2 505: indeed, 2 505 = 501 × 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 501). 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 22.383). 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 501

Preceding numbers: …499, 500
Following numbers: 502, 503…

Nearest numbers from 501

Preceding prime number: 499
Following prime number: 503