Is 687 a prime number?

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

For 687, the answer is: No, 687 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 687) is as follows: 1, 3, 229, 687.

For 687 to be a prime number, it would have been required that 687 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

687 is a multiple of 1
687 is a multiple of 3
687 is a multiple of 229

For 687 to be a prime number, it would have been required that 687 has only two divisors, i.e., itself and 1.

However, 687 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 687 = 3 x 229, where 3 and 229 are both prime numbers.

Is 687 a deficient number?

Yes, 687 is a deficient number, that is to say 687 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 687 without 687 itself (that is 1 + 3 + 229 = 233).

Parity of 687

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

Find out more:

What is an even number?

Is 687 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 687 is about 26.211.

Thus, the square root of 687 is not an integer, and therefore 687 is not a square number.

What is the square number of 687?

The square of a number (here 687) is the result of the product of this number (687) by itself (i.e., 687 × 687); the square of 687 is sometimes called "raising 687 to the power 2", or "687 squared".

The square of 687 is 471 969 because 687 × 687 = 687² = 471 969.

As a consequence, 687 is the square root of 471 969.

Number of digits of 687

687 is a number with 3 digits.

What are the multiples of 687?

The multiples of 687 are all integers evenly divisible by 687, that is all numbers such that the remainder of the division by 687 is zero. There are infinitely many multiples of 687. The smallest multiples of 687 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 687 too, since 0 × 687 = 0
687: indeed, 687 is a multiple of itself, since 687 is evenly divisible by 687 (we have 687 / 687 = 1, so the remainder of this division is indeed zero)
1 374: indeed, 1 374 = 687 × 2
2 061: indeed, 2 061 = 687 × 3
2 748: indeed, 2 748 = 687 × 4
3 435: indeed, 3 435 = 687 × 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 687). 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 26.211). 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 687

Preceding numbers: …685, 686
Following numbers: 688, 689…

Nearest numbers from 687

Preceding prime number: 683
Following prime number: 691