Is 666 a prime number?

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

For 666, the answer is: No, 666 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 666) is as follows: 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.

For 666 to be a prime number, it would have been required that 666 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

666 is a multiple of 1
666 is a multiple of 2
666 is a multiple of 3
666 is a multiple of 6
666 is a multiple of 9
666 is a multiple of 18
666 is a multiple of 37
666 is a multiple of 74
666 is a multiple of 111
666 is a multiple of 222
666 is a multiple of 333

For 666 to be a prime number, it would have been required that 666 has only two divisors, i.e., itself and 1.

Is 666 a deficient number?

No, 666 is not a deficient number: to be deficient, 666 should have been such that 666 is larger than the sum of its proper divisors, i.e., the divisors of 666 without 666 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 37 + 74 + 111 + 222 + 333 = 816).

In fact, 666 is an abundant number; 666 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 37 + 74 + 111 + 222 + 333 = 816). The smallest abundant number is 12.

Parity of 666

666 is an even number, because it is evenly divisible by 2: 666 / 2 = 333.

Find out more:

What is an even number?

Is 666 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 666 is about 25.807.

Thus, the square root of 666 is not an integer, and therefore 666 is not a square number.

What is the square number of 666?

The square of a number (here 666) is the result of the product of this number (666) by itself (i.e., 666 × 666); the square of 666 is sometimes called "raising 666 to the power 2", or "666 squared".

The square of 666 is 443 556 because 666 × 666 = 666² = 443 556.

As a consequence, 666 is the square root of 443 556.

Number of digits of 666

666 is a number with 3 digits.

What are the multiples of 666?

The multiples of 666 are all integers evenly divisible by 666, that is all numbers such that the remainder of the division by 666 is zero. There are infinitely many multiples of 666. The smallest multiples of 666 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 666 too, since 0 × 666 = 0
666: indeed, 666 is a multiple of itself, since 666 is evenly divisible by 666 (we have 666 / 666 = 1, so the remainder of this division is indeed zero)
1 332: indeed, 1 332 = 666 × 2
1 998: indeed, 1 998 = 666 × 3
2 664: indeed, 2 664 = 666 × 4
3 330: indeed, 3 330 = 666 × 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 666). 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 25.807). 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 666

Preceding numbers: …664, 665
Following numbers: 667, 668…

Nearest numbers from 666

Preceding prime number: 661
Following prime number: 673