Is 820 a prime number?

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

For 820, the answer is: No, 820 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 820) is as follows: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820.

For 820 to be a prime number, it would have been required that 820 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 820 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 820 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

820 is a multiple of 1
820 is a multiple of 2
820 is a multiple of 4
820 is a multiple of 5
820 is a multiple of 10
820 is a multiple of 20
820 is a multiple of 41
820 is a multiple of 82
820 is a multiple of 164
820 is a multiple of 205
820 is a multiple of 410

For 820 to be a prime number, it would have been required that 820 has only two divisors, i.e., itself and 1.

Is 820 a deficient number?

No, 820 is not a deficient number: to be deficient, 820 should have been such that 820 is larger than the sum of its proper divisors, i.e., the divisors of 820 without 820 itself (that is 1 + 2 + 4 + 5 + 10 + 20 + 41 + 82 + 164 + 205 + 410 = 944).

In fact, 820 is an abundant number; 820 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 + 20 + 41 + 82 + 164 + 205 + 410 = 944). The smallest abundant number is 12.

Parity of 820

820 is an even number, because it is evenly divisible by 2: 820 / 2 = 410.

Find out more:

What is an even number?

Is 820 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 820 is about 28.636.

Thus, the square root of 820 is not an integer, and therefore 820 is not a square number.

What is the square number of 820?

The square of a number (here 820) is the result of the product of this number (820) by itself (i.e., 820 × 820); the square of 820 is sometimes called "raising 820 to the power 2", or "820 squared".

The square of 820 is 672 400 because 820 × 820 = 820² = 672 400.

As a consequence, 820 is the square root of 672 400.

Number of digits of 820

820 is a number with 3 digits.

What are the multiples of 820?

The multiples of 820 are all integers evenly divisible by 820, that is all numbers such that the remainder of the division by 820 is zero. There are infinitely many multiples of 820. The smallest multiples of 820 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 820 too, since 0 × 820 = 0
820: indeed, 820 is a multiple of itself, since 820 is evenly divisible by 820 (we have 820 / 820 = 1, so the remainder of this division is indeed zero)
1 640: indeed, 1 640 = 820 × 2
2 460: indeed, 2 460 = 820 × 3
3 280: indeed, 3 280 = 820 × 4
4 100: indeed, 4 100 = 820 × 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 820). 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 28.636). 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 820

Preceding numbers: …818, 819
Following numbers: 821, 822…

Nearest numbers from 820

Preceding prime number: 811
Following prime number: 821