Is 338 a prime number?

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

For 338, the answer is: No, 338 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 338) is as follows: 1, 2, 13, 26, 169, 338.

For 338 to be a prime number, it would have been required that 338 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

338 is a multiple of 1
338 is a multiple of 2
338 is a multiple of 13
338 is a multiple of 26
338 is a multiple of 169

For 338 to be a prime number, it would have been required that 338 has only two divisors, i.e., itself and 1.

Is 338 a deficient number?

Yes, 338 is a deficient number, that is to say 338 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 338 without 338 itself (that is 1 + 2 + 13 + 26 + 169 = 211).

Parity of 338

338 is an even number, because it is evenly divisible by 2: 338 / 2 = 169.

Find out more:

What is an even number?

Is 338 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 338 is about 18.385.

Thus, the square root of 338 is not an integer, and therefore 338 is not a square number.

What is the square number of 338?

The square of a number (here 338) is the result of the product of this number (338) by itself (i.e., 338 × 338); the square of 338 is sometimes called "raising 338 to the power 2", or "338 squared".

The square of 338 is 114 244 because 338 × 338 = 338² = 114 244.

As a consequence, 338 is the square root of 114 244.

Number of digits of 338

338 is a number with 3 digits.

What are the multiples of 338?

The multiples of 338 are all integers evenly divisible by 338, that is all numbers such that the remainder of the division by 338 is zero. There are infinitely many multiples of 338. The smallest multiples of 338 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 338 too, since 0 × 338 = 0
338: indeed, 338 is a multiple of itself, since 338 is evenly divisible by 338 (we have 338 / 338 = 1, so the remainder of this division is indeed zero)
676: indeed, 676 = 338 × 2
1 014: indeed, 1 014 = 338 × 3
1 352: indeed, 1 352 = 338 × 4
1 690: indeed, 1 690 = 338 × 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 338). 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 18.385). 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 338

Preceding numbers: …336, 337
Following numbers: 339, 340…

Nearest numbers from 338

Preceding prime number: 337
Following prime number: 347