Is 800 a prime number?

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

For 800, the answer is: No, 800 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 800) is as follows: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.

For 800 to be a prime number, it would have been required that 800 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 800 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 800 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

800 is a multiple of 1
800 is a multiple of 2
800 is a multiple of 4
800 is a multiple of 5
800 is a multiple of 8
800 is a multiple of 10
800 is a multiple of 16
800 is a multiple of 20
800 is a multiple of 25
800 is a multiple of 32
800 is a multiple of 40
800 is a multiple of 50
800 is a multiple of 80
800 is a multiple of 100
800 is a multiple of 160
800 is a multiple of 200
800 is a multiple of 400

For 800 to be a prime number, it would have been required that 800 has only two divisors, i.e., itself and 1.

Is 800 a deficient number?

No, 800 is not a deficient number: to be deficient, 800 should have been such that 800 is larger than the sum of its proper divisors, i.e., the divisors of 800 without 800 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 80 + 100 + 160 + 200 + 400 = 1 153).

In fact, 800 is an abundant number; 800 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 80 + 100 + 160 + 200 + 400 = 1 153). The smallest abundant number is 12.

Parity of 800

800 is an even number, because it is evenly divisible by 2: 800 / 2 = 400.

Find out more:

What is an even number?

Is 800 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 800 is about 28.284.

Thus, the square root of 800 is not an integer, and therefore 800 is not a square number.

What is the square number of 800?

The square of a number (here 800) is the result of the product of this number (800) by itself (i.e., 800 × 800); the square of 800 is sometimes called "raising 800 to the power 2", or "800 squared".

The square of 800 is 640 000 because 800 × 800 = 800² = 640 000.

As a consequence, 800 is the square root of 640 000.

Number of digits of 800

800 is a number with 3 digits.

What are the multiples of 800?

The multiples of 800 are all integers evenly divisible by 800, that is all numbers such that the remainder of the division by 800 is zero. There are infinitely many multiples of 800. The smallest multiples of 800 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 800 too, since 0 × 800 = 0
800: indeed, 800 is a multiple of itself, since 800 is evenly divisible by 800 (we have 800 / 800 = 1, so the remainder of this division is indeed zero)
1 600: indeed, 1 600 = 800 × 2
2 400: indeed, 2 400 = 800 × 3
3 200: indeed, 3 200 = 800 × 4
4 000: indeed, 4 000 = 800 × 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 800). 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 28.284). 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 800

Preceding numbers: …798, 799
Following numbers: 801, 802…

Nearest numbers from 800

Preceding prime number: 797
Following prime number: 809