Is 686 a prime number?

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

For 686, the answer is: No, 686 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 686) is as follows: 1, 2, 7, 14, 49, 98, 343, 686.

For 686 to be a prime number, it would have been required that 686 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

686 is a multiple of 1
686 is a multiple of 2
686 is a multiple of 7
686 is a multiple of 14
686 is a multiple of 49
686 is a multiple of 98
686 is a multiple of 343

For 686 to be a prime number, it would have been required that 686 has only two divisors, i.e., itself and 1.

Is 686 a deficient number?

Yes, 686 is a deficient number, that is to say 686 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 686 without 686 itself (that is 1 + 2 + 7 + 14 + 49 + 98 + 343 = 514).

Parity of 686

686 is an even number, because it is evenly divisible by 2: 686 / 2 = 343.

Find out more:

What is an even number?

Is 686 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 686 is about 26.192.

Thus, the square root of 686 is not an integer, and therefore 686 is not a square number.

What is the square number of 686?

The square of a number (here 686) is the result of the product of this number (686) by itself (i.e., 686 × 686); the square of 686 is sometimes called "raising 686 to the power 2", or "686 squared".

The square of 686 is 470 596 because 686 × 686 = 686² = 470 596.

As a consequence, 686 is the square root of 470 596.

Number of digits of 686

686 is a number with 3 digits.

What are the multiples of 686?

The multiples of 686 are all integers evenly divisible by 686, that is all numbers such that the remainder of the division by 686 is zero. There are infinitely many multiples of 686. The smallest multiples of 686 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 686 too, since 0 × 686 = 0
686: indeed, 686 is a multiple of itself, since 686 is evenly divisible by 686 (we have 686 / 686 = 1, so the remainder of this division is indeed zero)
1 372: indeed, 1 372 = 686 × 2
2 058: indeed, 2 058 = 686 × 3
2 744: indeed, 2 744 = 686 × 4
3 430: indeed, 3 430 = 686 × 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 686). 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 26.192). 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 686

Preceding numbers: …684, 685
Following numbers: 687, 688…

Nearest numbers from 686

Preceding prime number: 683
Following prime number: 691