Is 38 a prime number?

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

For 38, the answer is: No, 38 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 38) is as follows: 1, 2, 19, 38.

For 38 to be a prime number, it would have been required that 38 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

38 is a multiple of 1
38 is a multiple of 2
38 is a multiple of 19

For 38 to be a prime number, it would have been required that 38 has only two divisors, i.e., itself and 1.

However, 38 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 38 = 2 x 19, where 2 and 19 are both prime numbers.

Is 38 a deficient number?

Yes, 38 is a deficient number, that is to say 38 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 38 without 38 itself (that is 1 + 2 + 19 = 22).

Parity of 38

38 is an even number, because it is evenly divisible by 2: 38 / 2 = 19.

Find out more:

What is an even number?

Is 38 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 38 is about 6.164.

Thus, the square root of 38 is not an integer, and therefore 38 is not a square number.

What is the square number of 38?

The square of a number (here 38) is the result of the product of this number (38) by itself (i.e., 38 × 38); the square of 38 is sometimes called "raising 38 to the power 2", or "38 squared".

The square of 38 is 1 444 because 38 × 38 = 38² = 1 444.

As a consequence, 38 is the square root of 1 444.

Number of digits of 38

38 is a number with 2 digits.

What are the multiples of 38?

The multiples of 38 are all integers evenly divisible by 38, that is all numbers such that the remainder of the division by 38 is zero. There are infinitely many multiples of 38. The smallest multiples of 38 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 38 too, since 0 × 38 = 0
38: indeed, 38 is a multiple of itself, since 38 is evenly divisible by 38 (we have 38 / 38 = 1, so the remainder of this division is indeed zero)
76: indeed, 76 = 38 × 2
114: indeed, 114 = 38 × 3
152: indeed, 152 = 38 × 4
190: indeed, 190 = 38 × 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 38). 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 6.164). 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 38

Preceding numbers: …36, 37
Following numbers: 39, 40…

Nearest numbers from 38

Preceding prime number: 37
Following prime number: 41