Is 685 a prime number?

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

For 685, the answer is: No, 685 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 685) is as follows: 1, 5, 137, 685.

For 685 to be a prime number, it would have been required that 685 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 685 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 685 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

685 is a multiple of 1
685 is a multiple of 5
685 is a multiple of 137

For 685 to be a prime number, it would have been required that 685 has only two divisors, i.e., itself and 1.

However, 685 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 685 = 5 x 137, where 5 and 137 are both prime numbers.

Is 685 a deficient number?

Yes, 685 is a deficient number, that is to say 685 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 685 without 685 itself (that is 1 + 5 + 137 = 143).

Parity of 685

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

Find out more:

What is an even number?

Is 685 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 685 is about 26.173.

Thus, the square root of 685 is not an integer, and therefore 685 is not a square number.

What is the square number of 685?

The square of a number (here 685) is the result of the product of this number (685) by itself (i.e., 685 × 685); the square of 685 is sometimes called "raising 685 to the power 2", or "685 squared".

The square of 685 is 469 225 because 685 × 685 = 685² = 469 225.

As a consequence, 685 is the square root of 469 225.

Number of digits of 685

685 is a number with 3 digits.

What are the multiples of 685?

The multiples of 685 are all integers evenly divisible by 685, that is all numbers such that the remainder of the division by 685 is zero. There are infinitely many multiples of 685. The smallest multiples of 685 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 685 too, since 0 × 685 = 0
685: indeed, 685 is a multiple of itself, since 685 is evenly divisible by 685 (we have 685 / 685 = 1, so the remainder of this division is indeed zero)
1 370: indeed, 1 370 = 685 × 2
2 055: indeed, 2 055 = 685 × 3
2 740: indeed, 2 740 = 685 × 4
3 425: indeed, 3 425 = 685 × 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 685). 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 26.173). 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 685

Preceding numbers: …683, 684
Following numbers: 686, 687…

Nearest numbers from 685

Preceding prime number: 683
Following prime number: 691