Is 638 a prime number?

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

For 638, the answer is: No, 638 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 638) is as follows: 1, 2, 11, 22, 29, 58, 319, 638.

For 638 to be a prime number, it would have been required that 638 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

638 is a multiple of 1
638 is a multiple of 2
638 is a multiple of 11
638 is a multiple of 22
638 is a multiple of 29
638 is a multiple of 58
638 is a multiple of 319

For 638 to be a prime number, it would have been required that 638 has only two divisors, i.e., itself and 1.

Is 638 a deficient number?

Yes, 638 is a deficient number, that is to say 638 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 638 without 638 itself (that is 1 + 2 + 11 + 22 + 29 + 58 + 319 = 442).

Parity of 638

638 is an even number, because it is evenly divisible by 2: 638 / 2 = 319.

Find out more:

What is an even number?

Is 638 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 638 is about 25.259.

Thus, the square root of 638 is not an integer, and therefore 638 is not a square number.

What is the square number of 638?

The square of a number (here 638) is the result of the product of this number (638) by itself (i.e., 638 × 638); the square of 638 is sometimes called "raising 638 to the power 2", or "638 squared".

The square of 638 is 407 044 because 638 × 638 = 638² = 407 044.

As a consequence, 638 is the square root of 407 044.

Number of digits of 638

638 is a number with 3 digits.

What are the multiples of 638?

The multiples of 638 are all integers evenly divisible by 638, that is all numbers such that the remainder of the division by 638 is zero. There are infinitely many multiples of 638. The smallest multiples of 638 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 638 too, since 0 × 638 = 0
638: indeed, 638 is a multiple of itself, since 638 is evenly divisible by 638 (we have 638 / 638 = 1, so the remainder of this division is indeed zero)
1 276: indeed, 1 276 = 638 × 2
1 914: indeed, 1 914 = 638 × 3
2 552: indeed, 2 552 = 638 × 4
3 190: indeed, 3 190 = 638 × 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 638). 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 25.259). 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 638

Preceding numbers: …636, 637
Following numbers: 639, 640…

Nearest numbers from 638

Preceding prime number: 631
Following prime number: 641