Is 852 a prime number?

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

For 852, the answer is: No, 852 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 852) is as follows: 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852.

For 852 to be a prime number, it would have been required that 852 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

852 is a multiple of 1
852 is a multiple of 2
852 is a multiple of 3
852 is a multiple of 4
852 is a multiple of 6
852 is a multiple of 12
852 is a multiple of 71
852 is a multiple of 142
852 is a multiple of 213
852 is a multiple of 284
852 is a multiple of 426

For 852 to be a prime number, it would have been required that 852 has only two divisors, i.e., itself and 1.

Is 852 a deficient number?

No, 852 is not a deficient number: to be deficient, 852 should have been such that 852 is larger than the sum of its proper divisors, i.e., the divisors of 852 without 852 itself (that is 1 + 2 + 3 + 4 + 6 + 12 + 71 + 142 + 213 + 284 + 426 = 1 164).

In fact, 852 is an abundant number; 852 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 12 + 71 + 142 + 213 + 284 + 426 = 1 164). The smallest abundant number is 12.

Parity of 852

852 is an even number, because it is evenly divisible by 2: 852 / 2 = 426.

Find out more:

What is an even number?

Is 852 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 852 is about 29.189.

Thus, the square root of 852 is not an integer, and therefore 852 is not a square number.

What is the square number of 852?

The square of a number (here 852) is the result of the product of this number (852) by itself (i.e., 852 × 852); the square of 852 is sometimes called "raising 852 to the power 2", or "852 squared".

The square of 852 is 725 904 because 852 × 852 = 852² = 725 904.

As a consequence, 852 is the square root of 725 904.

Number of digits of 852

852 is a number with 3 digits.

What are the multiples of 852?

The multiples of 852 are all integers evenly divisible by 852, that is all numbers such that the remainder of the division by 852 is zero. There are infinitely many multiples of 852. The smallest multiples of 852 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 852 too, since 0 × 852 = 0
852: indeed, 852 is a multiple of itself, since 852 is evenly divisible by 852 (we have 852 / 852 = 1, so the remainder of this division is indeed zero)
1 704: indeed, 1 704 = 852 × 2
2 556: indeed, 2 556 = 852 × 3
3 408: indeed, 3 408 = 852 × 4
4 260: indeed, 4 260 = 852 × 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 852). 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 29.189). 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 852

Preceding numbers: …850, 851
Following numbers: 853, 854…

Nearest numbers from 852

Preceding prime number: 839
Following prime number: 853