Is 663 a prime number?

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

For 663, the answer is: No, 663 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 663) is as follows: 1, 3, 13, 17, 39, 51, 221, 663.

For 663 to be a prime number, it would have been required that 663 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

663 is a multiple of 1
663 is a multiple of 3
663 is a multiple of 13
663 is a multiple of 17
663 is a multiple of 39
663 is a multiple of 51
663 is a multiple of 221

For 663 to be a prime number, it would have been required that 663 has only two divisors, i.e., itself and 1.

Is 663 a deficient number?

Yes, 663 is a deficient number, that is to say 663 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 663 without 663 itself (that is 1 + 3 + 13 + 17 + 39 + 51 + 221 = 345).

Parity of 663

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

Find out more:

What is an even number?

Is 663 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 663 is about 25.749.

Thus, the square root of 663 is not an integer, and therefore 663 is not a square number.

What is the square number of 663?

The square of a number (here 663) is the result of the product of this number (663) by itself (i.e., 663 × 663); the square of 663 is sometimes called "raising 663 to the power 2", or "663 squared".

The square of 663 is 439 569 because 663 × 663 = 663² = 439 569.

As a consequence, 663 is the square root of 439 569.

Number of digits of 663

663 is a number with 3 digits.

What are the multiples of 663?

The multiples of 663 are all integers evenly divisible by 663, that is all numbers such that the remainder of the division by 663 is zero. There are infinitely many multiples of 663. The smallest multiples of 663 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 663 too, since 0 × 663 = 0
663: indeed, 663 is a multiple of itself, since 663 is evenly divisible by 663 (we have 663 / 663 = 1, so the remainder of this division is indeed zero)
1 326: indeed, 1 326 = 663 × 2
1 989: indeed, 1 989 = 663 × 3
2 652: indeed, 2 652 = 663 × 4
3 315: indeed, 3 315 = 663 × 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 663). 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 25.749). 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 663

Preceding numbers: …661, 662
Following numbers: 664, 665…

Nearest numbers from 663

Preceding prime number: 661
Following prime number: 673