Is 897 a prime number?

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

For 897, the answer is: No, 897 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 897) is as follows: 1, 3, 13, 23, 39, 69, 299, 897.

For 897 to be a prime number, it would have been required that 897 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

897 is a multiple of 1
897 is a multiple of 3
897 is a multiple of 13
897 is a multiple of 23
897 is a multiple of 39
897 is a multiple of 69
897 is a multiple of 299

For 897 to be a prime number, it would have been required that 897 has only two divisors, i.e., itself and 1.

Is 897 a deficient number?

Yes, 897 is a deficient number, that is to say 897 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 897 without 897 itself (that is 1 + 3 + 13 + 23 + 39 + 69 + 299 = 447).

Parity of 897

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

Find out more:

What is an even number?

Is 897 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 897 is about 29.950.

Thus, the square root of 897 is not an integer, and therefore 897 is not a square number.

What is the square number of 897?

The square of a number (here 897) is the result of the product of this number (897) by itself (i.e., 897 × 897); the square of 897 is sometimes called "raising 897 to the power 2", or "897 squared".

The square of 897 is 804 609 because 897 × 897 = 897² = 804 609.

As a consequence, 897 is the square root of 804 609.

Number of digits of 897

897 is a number with 3 digits.

What are the multiples of 897?

The multiples of 897 are all integers evenly divisible by 897, that is all numbers such that the remainder of the division by 897 is zero. There are infinitely many multiples of 897. The smallest multiples of 897 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 897 too, since 0 × 897 = 0
897: indeed, 897 is a multiple of itself, since 897 is evenly divisible by 897 (we have 897 / 897 = 1, so the remainder of this division is indeed zero)
1 794: indeed, 1 794 = 897 × 2
2 691: indeed, 2 691 = 897 × 3
3 588: indeed, 3 588 = 897 × 4
4 485: indeed, 4 485 = 897 × 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 897). 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 29.950). 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 897

Preceding numbers: …895, 896
Following numbers: 898, 899…

Nearest numbers from 897

Preceding prime number: 887
Following prime number: 907