Is 688 a prime number?

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

For 688, the answer is: No, 688 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 688) is as follows: 1, 2, 4, 8, 16, 43, 86, 172, 344, 688.

For 688 to be a prime number, it would have been required that 688 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

688 is a multiple of 1
688 is a multiple of 2
688 is a multiple of 4
688 is a multiple of 8
688 is a multiple of 16
688 is a multiple of 43
688 is a multiple of 86
688 is a multiple of 172
688 is a multiple of 344

For 688 to be a prime number, it would have been required that 688 has only two divisors, i.e., itself and 1.

Is 688 a deficient number?

Yes, 688 is a deficient number, that is to say 688 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 688 without 688 itself (that is 1 + 2 + 4 + 8 + 16 + 43 + 86 + 172 + 344 = 676).

Parity of 688

688 is an even number, because it is evenly divisible by 2: 688 / 2 = 344.

Find out more:

What is an even number?

Is 688 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 688 is about 26.230.

Thus, the square root of 688 is not an integer, and therefore 688 is not a square number.

What is the square number of 688?

The square of a number (here 688) is the result of the product of this number (688) by itself (i.e., 688 × 688); the square of 688 is sometimes called "raising 688 to the power 2", or "688 squared".

The square of 688 is 473 344 because 688 × 688 = 688² = 473 344.

As a consequence, 688 is the square root of 473 344.

Number of digits of 688

688 is a number with 3 digits.

What are the multiples of 688?

The multiples of 688 are all integers evenly divisible by 688, that is all numbers such that the remainder of the division by 688 is zero. There are infinitely many multiples of 688. The smallest multiples of 688 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 688 too, since 0 × 688 = 0
688: indeed, 688 is a multiple of itself, since 688 is evenly divisible by 688 (we have 688 / 688 = 1, so the remainder of this division is indeed zero)
1 376: indeed, 1 376 = 688 × 2
2 064: indeed, 2 064 = 688 × 3
2 752: indeed, 2 752 = 688 × 4
3 440: indeed, 3 440 = 688 × 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 688). 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 26.230). 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 688

Preceding numbers: …686, 687
Following numbers: 689, 690…

Nearest numbers from 688

Preceding prime number: 683
Following prime number: 691