Is 684 a prime number?

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

For 684, the answer is: No, 684 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 684) is as follows: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684.

For 684 to be a prime number, it would have been required that 684 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

684 is a multiple of 1
684 is a multiple of 2
684 is a multiple of 3
684 is a multiple of 4
684 is a multiple of 6
684 is a multiple of 9
684 is a multiple of 12
684 is a multiple of 18
684 is a multiple of 19
684 is a multiple of 36
684 is a multiple of 38
684 is a multiple of 57
684 is a multiple of 76
684 is a multiple of 114
684 is a multiple of 171
684 is a multiple of 228
684 is a multiple of 342

For 684 to be a prime number, it would have been required that 684 has only two divisors, i.e., itself and 1.

Is 684 a deficient number?

No, 684 is not a deficient number: to be deficient, 684 should have been such that 684 is larger than the sum of its proper divisors, i.e., the divisors of 684 without 684 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 19 + 36 + 38 + 57 + 76 + 114 + 171 + 228 + 342 = 1 136).

In fact, 684 is an abundant number; 684 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 19 + 36 + 38 + 57 + 76 + 114 + 171 + 228 + 342 = 1 136). The smallest abundant number is 12.

Parity of 684

684 is an even number, because it is evenly divisible by 2: 684 / 2 = 342.

Find out more:

What is an even number?

Is 684 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 684 is about 26.153.

Thus, the square root of 684 is not an integer, and therefore 684 is not a square number.

What is the square number of 684?

The square of a number (here 684) is the result of the product of this number (684) by itself (i.e., 684 × 684); the square of 684 is sometimes called "raising 684 to the power 2", or "684 squared".

The square of 684 is 467 856 because 684 × 684 = 684² = 467 856.

As a consequence, 684 is the square root of 467 856.

Number of digits of 684

684 is a number with 3 digits.

What are the multiples of 684?

The multiples of 684 are all integers evenly divisible by 684, that is all numbers such that the remainder of the division by 684 is zero. There are infinitely many multiples of 684. The smallest multiples of 684 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 684 too, since 0 × 684 = 0
684: indeed, 684 is a multiple of itself, since 684 is evenly divisible by 684 (we have 684 / 684 = 1, so the remainder of this division is indeed zero)
1 368: indeed, 1 368 = 684 × 2
2 052: indeed, 2 052 = 684 × 3
2 736: indeed, 2 736 = 684 × 4
3 420: indeed, 3 420 = 684 × 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 684). 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 26.153). 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 684

Preceding numbers: …682, 683
Following numbers: 685, 686…

Nearest numbers from 684

Preceding prime number: 683
Following prime number: 691