Is 851 a prime number?

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

For 851, the answer is: No, 851 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 851) is as follows: 1, 23, 37, 851.

For 851 to be a prime number, it would have been required that 851 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

851 is a multiple of 1
851 is a multiple of 23
851 is a multiple of 37

For 851 to be a prime number, it would have been required that 851 has only two divisors, i.e., itself and 1.

However, 851 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 851 = 23 x 37, where 23 and 37 are both prime numbers.

Is 851 a deficient number?

Yes, 851 is a deficient number, that is to say 851 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 851 without 851 itself (that is 1 + 23 + 37 = 61).

Parity of 851

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

Find out more:

What is an even number?

Is 851 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 851 is about 29.172.

Thus, the square root of 851 is not an integer, and therefore 851 is not a square number.

What is the square number of 851?

The square of a number (here 851) is the result of the product of this number (851) by itself (i.e., 851 × 851); the square of 851 is sometimes called "raising 851 to the power 2", or "851 squared".

The square of 851 is 724 201 because 851 × 851 = 851² = 724 201.

As a consequence, 851 is the square root of 724 201.

Number of digits of 851

851 is a number with 3 digits.

What are the multiples of 851?

The multiples of 851 are all integers evenly divisible by 851, that is all numbers such that the remainder of the division by 851 is zero. There are infinitely many multiples of 851. The smallest multiples of 851 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 851 too, since 0 × 851 = 0
851: indeed, 851 is a multiple of itself, since 851 is evenly divisible by 851 (we have 851 / 851 = 1, so the remainder of this division is indeed zero)
1 702: indeed, 1 702 = 851 × 2
2 553: indeed, 2 553 = 851 × 3
3 404: indeed, 3 404 = 851 × 4
4 255: indeed, 4 255 = 851 × 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 851). 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 29.172). 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 851

Preceding numbers: …849, 850
Following numbers: 852, 853…

Nearest numbers from 851

Preceding prime number: 839
Following prime number: 853