Is 801 a prime number?

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

For 801, the answer is: No, 801 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 801) is as follows: 1, 3, 9, 89, 267, 801.

For 801 to be a prime number, it would have been required that 801 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

801 is a multiple of 1
801 is a multiple of 3
801 is a multiple of 9
801 is a multiple of 89
801 is a multiple of 267

For 801 to be a prime number, it would have been required that 801 has only two divisors, i.e., itself and 1.

Is 801 a deficient number?

Yes, 801 is a deficient number, that is to say 801 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 801 without 801 itself (that is 1 + 3 + 9 + 89 + 267 = 369).

Parity of 801

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

Find out more:

What is an even number?

Is 801 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 801 is about 28.302.

Thus, the square root of 801 is not an integer, and therefore 801 is not a square number.

What is the square number of 801?

The square of a number (here 801) is the result of the product of this number (801) by itself (i.e., 801 × 801); the square of 801 is sometimes called "raising 801 to the power 2", or "801 squared".

The square of 801 is 641 601 because 801 × 801 = 801² = 641 601.

As a consequence, 801 is the square root of 641 601.

Number of digits of 801

801 is a number with 3 digits.

What are the multiples of 801?

The multiples of 801 are all integers evenly divisible by 801, that is all numbers such that the remainder of the division by 801 is zero. There are infinitely many multiples of 801. The smallest multiples of 801 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 801 too, since 0 × 801 = 0
801: indeed, 801 is a multiple of itself, since 801 is evenly divisible by 801 (we have 801 / 801 = 1, so the remainder of this division is indeed zero)
1 602: indeed, 1 602 = 801 × 2
2 403: indeed, 2 403 = 801 × 3
3 204: indeed, 3 204 = 801 × 4
4 005: indeed, 4 005 = 801 × 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 801). 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 28.302). 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 801

Preceding numbers: …799, 800
Following numbers: 802, 803…

Nearest numbers from 801

Preceding prime number: 797
Following prime number: 809