Is 689 a prime number?

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

For 689, the answer is: No, 689 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 689) is as follows: 1, 13, 53, 689.

For 689 to be a prime number, it would have been required that 689 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

689 is a multiple of 1
689 is a multiple of 13
689 is a multiple of 53

For 689 to be a prime number, it would have been required that 689 has only two divisors, i.e., itself and 1.

However, 689 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 689 = 13 x 53, where 13 and 53 are both prime numbers.

Is 689 a deficient number?

Yes, 689 is a deficient number, that is to say 689 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 689 without 689 itself (that is 1 + 13 + 53 = 67).

Parity of 689

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

Find out more:

What is an even number?

Is 689 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 689 is about 26.249.

Thus, the square root of 689 is not an integer, and therefore 689 is not a square number.

What is the square number of 689?

The square of a number (here 689) is the result of the product of this number (689) by itself (i.e., 689 × 689); the square of 689 is sometimes called "raising 689 to the power 2", or "689 squared".

The square of 689 is 474 721 because 689 × 689 = 689² = 474 721.

As a consequence, 689 is the square root of 474 721.

Number of digits of 689

689 is a number with 3 digits.

What are the multiples of 689?

The multiples of 689 are all integers evenly divisible by 689, that is all numbers such that the remainder of the division by 689 is zero. There are infinitely many multiples of 689. The smallest multiples of 689 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 689 too, since 0 × 689 = 0
689: indeed, 689 is a multiple of itself, since 689 is evenly divisible by 689 (we have 689 / 689 = 1, so the remainder of this division is indeed zero)
1 378: indeed, 1 378 = 689 × 2
2 067: indeed, 2 067 = 689 × 3
2 756: indeed, 2 756 = 689 × 4
3 445: indeed, 3 445 = 689 × 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 689). 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 26.249). 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 689

Preceding numbers: …687, 688
Following numbers: 690, 691…

Nearest numbers from 689

Preceding prime number: 683
Following prime number: 691