Is 803 a prime number?

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

For 803, the answer is: No, 803 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 803) is as follows: 1, 11, 73, 803.

For 803 to be a prime number, it would have been required that 803 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

803 is a multiple of 1
803 is a multiple of 11
803 is a multiple of 73

For 803 to be a prime number, it would have been required that 803 has only two divisors, i.e., itself and 1.

However, 803 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 803 = 11 x 73, where 11 and 73 are both prime numbers.

Is 803 a deficient number?

Yes, 803 is a deficient number, that is to say 803 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 803 without 803 itself (that is 1 + 11 + 73 = 85).

Parity of 803

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

Find out more:

What is an even number?

Is 803 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 803 is about 28.337.

Thus, the square root of 803 is not an integer, and therefore 803 is not a square number.

What is the square number of 803?

The square of a number (here 803) is the result of the product of this number (803) by itself (i.e., 803 × 803); the square of 803 is sometimes called "raising 803 to the power 2", or "803 squared".

The square of 803 is 644 809 because 803 × 803 = 803² = 644 809.

As a consequence, 803 is the square root of 644 809.

Number of digits of 803

803 is a number with 3 digits.

What are the multiples of 803?

The multiples of 803 are all integers evenly divisible by 803, that is all numbers such that the remainder of the division by 803 is zero. There are infinitely many multiples of 803. The smallest multiples of 803 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 803 too, since 0 × 803 = 0
803: indeed, 803 is a multiple of itself, since 803 is evenly divisible by 803 (we have 803 / 803 = 1, so the remainder of this division is indeed zero)
1 606: indeed, 1 606 = 803 × 2
2 409: indeed, 2 409 = 803 × 3
3 212: indeed, 3 212 = 803 × 4
4 015: indeed, 4 015 = 803 × 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 803). 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 28.337). 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 803

Preceding numbers: …801, 802
Following numbers: 804, 805…

Nearest numbers from 803

Preceding prime number: 797
Following prime number: 809