Is 838 a prime number?

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

For 838, the answer is: No, 838 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 838) is as follows: 1, 2, 419, 838.

For 838 to be a prime number, it would have been required that 838 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

838 is a multiple of 1
838 is a multiple of 2
838 is a multiple of 419

For 838 to be a prime number, it would have been required that 838 has only two divisors, i.e., itself and 1.

However, 838 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 838 = 2 x 419, where 2 and 419 are both prime numbers.

Is 838 a deficient number?

Yes, 838 is a deficient number, that is to say 838 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 838 without 838 itself (that is 1 + 2 + 419 = 422).

Parity of 838

838 is an even number, because it is evenly divisible by 2: 838 / 2 = 419.

Find out more:

What is an even number?

Is 838 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 838 is about 28.948.

Thus, the square root of 838 is not an integer, and therefore 838 is not a square number.

What is the square number of 838?

The square of a number (here 838) is the result of the product of this number (838) by itself (i.e., 838 × 838); the square of 838 is sometimes called "raising 838 to the power 2", or "838 squared".

The square of 838 is 702 244 because 838 × 838 = 838² = 702 244.

As a consequence, 838 is the square root of 702 244.

Number of digits of 838

838 is a number with 3 digits.

What are the multiples of 838?

The multiples of 838 are all integers evenly divisible by 838, that is all numbers such that the remainder of the division by 838 is zero. There are infinitely many multiples of 838. The smallest multiples of 838 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 838 too, since 0 × 838 = 0
838: indeed, 838 is a multiple of itself, since 838 is evenly divisible by 838 (we have 838 / 838 = 1, so the remainder of this division is indeed zero)
1 676: indeed, 1 676 = 838 × 2
2 514: indeed, 2 514 = 838 × 3
3 352: indeed, 3 352 = 838 × 4
4 190: indeed, 4 190 = 838 × 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 838). 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 28.948). 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 838

Preceding numbers: …836, 837
Following numbers: 839, 840…

Nearest numbers from 838

Preceding prime number: 829
Following prime number: 839