Is 802 a prime number?

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

For 802, the answer is: No, 802 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 802) is as follows: 1, 2, 401, 802.

For 802 to be a prime number, it would have been required that 802 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

802 is a multiple of 1
802 is a multiple of 2
802 is a multiple of 401

For 802 to be a prime number, it would have been required that 802 has only two divisors, i.e., itself and 1.

However, 802 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 802 = 2 x 401, where 2 and 401 are both prime numbers.

Is 802 a deficient number?

Yes, 802 is a deficient number, that is to say 802 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 802 without 802 itself (that is 1 + 2 + 401 = 404).

Parity of 802

802 is an even number, because it is evenly divisible by 2: 802 / 2 = 401.

Find out more:

What is an even number?

Is 802 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 802 is about 28.320.

Thus, the square root of 802 is not an integer, and therefore 802 is not a square number.

What is the square number of 802?

The square of a number (here 802) is the result of the product of this number (802) by itself (i.e., 802 × 802); the square of 802 is sometimes called "raising 802 to the power 2", or "802 squared".

The square of 802 is 643 204 because 802 × 802 = 802² = 643 204.

As a consequence, 802 is the square root of 643 204.

Number of digits of 802

802 is a number with 3 digits.

What are the multiples of 802?

The multiples of 802 are all integers evenly divisible by 802, that is all numbers such that the remainder of the division by 802 is zero. There are infinitely many multiples of 802. The smallest multiples of 802 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 802 too, since 0 × 802 = 0
802: indeed, 802 is a multiple of itself, since 802 is evenly divisible by 802 (we have 802 / 802 = 1, so the remainder of this division is indeed zero)
1 604: indeed, 1 604 = 802 × 2
2 406: indeed, 2 406 = 802 × 3
3 208: indeed, 3 208 = 802 × 4
4 010: indeed, 4 010 = 802 × 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 802). 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 28.320). 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 802

Preceding numbers: …800, 801
Following numbers: 803, 804…

Nearest numbers from 802

Preceding prime number: 797
Following prime number: 809