Is 681 a prime number?

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

For 681, the answer is: No, 681 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 681) is as follows: 1, 3, 227, 681.

For 681 to be a prime number, it would have been required that 681 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

681 is a multiple of 1
681 is a multiple of 3
681 is a multiple of 227

For 681 to be a prime number, it would have been required that 681 has only two divisors, i.e., itself and 1.

However, 681 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 681 = 3 x 227, where 3 and 227 are both prime numbers.

Is 681 a deficient number?

Yes, 681 is a deficient number, that is to say 681 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 681 without 681 itself (that is 1 + 3 + 227 = 231).

Parity of 681

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

Find out more:

What is an even number?

Is 681 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 681 is about 26.096.

Thus, the square root of 681 is not an integer, and therefore 681 is not a square number.

What is the square number of 681?

The square of a number (here 681) is the result of the product of this number (681) by itself (i.e., 681 × 681); the square of 681 is sometimes called "raising 681 to the power 2", or "681 squared".

The square of 681 is 463 761 because 681 × 681 = 681² = 463 761.

As a consequence, 681 is the square root of 463 761.

Number of digits of 681

681 is a number with 3 digits.

What are the multiples of 681?

The multiples of 681 are all integers evenly divisible by 681, that is all numbers such that the remainder of the division by 681 is zero. There are infinitely many multiples of 681. The smallest multiples of 681 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 681 too, since 0 × 681 = 0
681: indeed, 681 is a multiple of itself, since 681 is evenly divisible by 681 (we have 681 / 681 = 1, so the remainder of this division is indeed zero)
1 362: indeed, 1 362 = 681 × 2
2 043: indeed, 2 043 = 681 × 3
2 724: indeed, 2 724 = 681 × 4
3 405: indeed, 3 405 = 681 × 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 681). 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 26.096). 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 681

Preceding numbers: …679, 680
Following numbers: 682, 683…

Nearest numbers from 681

Preceding prime number: 677
Following prime number: 683