Is 678 a prime number?

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

For 678, the answer is: No, 678 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 678) is as follows: 1, 2, 3, 6, 113, 226, 339, 678.

For 678 to be a prime number, it would have been required that 678 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

678 is a multiple of 1
678 is a multiple of 2
678 is a multiple of 3
678 is a multiple of 6
678 is a multiple of 113
678 is a multiple of 226
678 is a multiple of 339

For 678 to be a prime number, it would have been required that 678 has only two divisors, i.e., itself and 1.

Is 678 a deficient number?

No, 678 is not a deficient number: to be deficient, 678 should have been such that 678 is larger than the sum of its proper divisors, i.e., the divisors of 678 without 678 itself (that is 1 + 2 + 3 + 6 + 113 + 226 + 339 = 690).

In fact, 678 is an abundant number; 678 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 113 + 226 + 339 = 690). The smallest abundant number is 12.

Parity of 678

678 is an even number, because it is evenly divisible by 2: 678 / 2 = 339.

Find out more:

What is an even number?

Is 678 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 678 is about 26.038.

Thus, the square root of 678 is not an integer, and therefore 678 is not a square number.

What is the square number of 678?

The square of a number (here 678) is the result of the product of this number (678) by itself (i.e., 678 × 678); the square of 678 is sometimes called "raising 678 to the power 2", or "678 squared".

The square of 678 is 459 684 because 678 × 678 = 678² = 459 684.

As a consequence, 678 is the square root of 459 684.

Number of digits of 678

678 is a number with 3 digits.

What are the multiples of 678?

The multiples of 678 are all integers evenly divisible by 678, that is all numbers such that the remainder of the division by 678 is zero. There are infinitely many multiples of 678. The smallest multiples of 678 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 678 too, since 0 × 678 = 0
678: indeed, 678 is a multiple of itself, since 678 is evenly divisible by 678 (we have 678 / 678 = 1, so the remainder of this division is indeed zero)
1 356: indeed, 1 356 = 678 × 2
2 034: indeed, 2 034 = 678 × 3
2 712: indeed, 2 712 = 678 × 4
3 390: indeed, 3 390 = 678 × 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 678). 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 26.038). 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 678

Preceding numbers: …676, 677
Following numbers: 679, 680…

Nearest numbers from 678

Preceding prime number: 677
Following prime number: 683