Is 849 a prime number?

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

For 849, the answer is: No, 849 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 849) is as follows: 1, 3, 283, 849.

For 849 to be a prime number, it would have been required that 849 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

849 is a multiple of 1
849 is a multiple of 3
849 is a multiple of 283

For 849 to be a prime number, it would have been required that 849 has only two divisors, i.e., itself and 1.

However, 849 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 849 = 3 x 283, where 3 and 283 are both prime numbers.

Is 849 a deficient number?

Yes, 849 is a deficient number, that is to say 849 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 849 without 849 itself (that is 1 + 3 + 283 = 287).

Parity of 849

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

Find out more:

What is an even number?

Is 849 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 849 is about 29.138.

Thus, the square root of 849 is not an integer, and therefore 849 is not a square number.

What is the square number of 849?

The square of a number (here 849) is the result of the product of this number (849) by itself (i.e., 849 × 849); the square of 849 is sometimes called "raising 849 to the power 2", or "849 squared".

The square of 849 is 720 801 because 849 × 849 = 849² = 720 801.

As a consequence, 849 is the square root of 720 801.

Number of digits of 849

849 is a number with 3 digits.

What are the multiples of 849?

The multiples of 849 are all integers evenly divisible by 849, that is all numbers such that the remainder of the division by 849 is zero. There are infinitely many multiples of 849. The smallest multiples of 849 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 849 too, since 0 × 849 = 0
849: indeed, 849 is a multiple of itself, since 849 is evenly divisible by 849 (we have 849 / 849 = 1, so the remainder of this division is indeed zero)
1 698: indeed, 1 698 = 849 × 2
2 547: indeed, 2 547 = 849 × 3
3 396: indeed, 3 396 = 849 × 4
4 245: indeed, 4 245 = 849 × 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 849). 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 29.138). 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 849

Preceding numbers: …847, 848
Following numbers: 850, 851…

Nearest numbers from 849

Preceding prime number: 839
Following prime number: 853