Is 680 a prime number?

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

For 680, the answer is: No, 680 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 680) is as follows: 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680.

For 680 to be a prime number, it would have been required that 680 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 680 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 680 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

680 is a multiple of 1
680 is a multiple of 2
680 is a multiple of 4
680 is a multiple of 5
680 is a multiple of 8
680 is a multiple of 10
680 is a multiple of 17
680 is a multiple of 20
680 is a multiple of 34
680 is a multiple of 40
680 is a multiple of 68
680 is a multiple of 85
680 is a multiple of 136
680 is a multiple of 170
680 is a multiple of 340

For 680 to be a prime number, it would have been required that 680 has only two divisors, i.e., itself and 1.

Is 680 a deficient number?

No, 680 is not a deficient number: to be deficient, 680 should have been such that 680 is larger than the sum of its proper divisors, i.e., the divisors of 680 without 680 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 34 + 40 + 68 + 85 + 136 + 170 + 340 = 940).

In fact, 680 is an abundant number; 680 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 17 + 20 + 34 + 40 + 68 + 85 + 136 + 170 + 340 = 940). The smallest abundant number is 12.

Parity of 680

680 is an even number, because it is evenly divisible by 2: 680 / 2 = 340.

Find out more:

What is an even number?

Is 680 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 680 is about 26.077.

Thus, the square root of 680 is not an integer, and therefore 680 is not a square number.

What is the square number of 680?

The square of a number (here 680) is the result of the product of this number (680) by itself (i.e., 680 × 680); the square of 680 is sometimes called "raising 680 to the power 2", or "680 squared".

The square of 680 is 462 400 because 680 × 680 = 680² = 462 400.

As a consequence, 680 is the square root of 462 400.

Number of digits of 680

680 is a number with 3 digits.

What are the multiples of 680?

The multiples of 680 are all integers evenly divisible by 680, that is all numbers such that the remainder of the division by 680 is zero. There are infinitely many multiples of 680. The smallest multiples of 680 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 680 too, since 0 × 680 = 0
680: indeed, 680 is a multiple of itself, since 680 is evenly divisible by 680 (we have 680 / 680 = 1, so the remainder of this division is indeed zero)
1 360: indeed, 1 360 = 680 × 2
2 040: indeed, 2 040 = 680 × 3
2 720: indeed, 2 720 = 680 × 4
3 400: indeed, 3 400 = 680 × 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 680). 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 26.077). 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 680

Preceding numbers: …678, 679
Following numbers: 681, 682…

Nearest numbers from 680

Preceding prime number: 677
Following prime number: 683