Is 834 a prime number?

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

For 834, the answer is: No, 834 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 834) is as follows: 1, 2, 3, 6, 139, 278, 417, 834.

For 834 to be a prime number, it would have been required that 834 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

834 is a multiple of 1
834 is a multiple of 2
834 is a multiple of 3
834 is a multiple of 6
834 is a multiple of 139
834 is a multiple of 278
834 is a multiple of 417

For 834 to be a prime number, it would have been required that 834 has only two divisors, i.e., itself and 1.

Is 834 a deficient number?

No, 834 is not a deficient number: to be deficient, 834 should have been such that 834 is larger than the sum of its proper divisors, i.e., the divisors of 834 without 834 itself (that is 1 + 2 + 3 + 6 + 139 + 278 + 417 = 846).

In fact, 834 is an abundant number; 834 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 139 + 278 + 417 = 846). The smallest abundant number is 12.

Parity of 834

834 is an even number, because it is evenly divisible by 2: 834 / 2 = 417.

Find out more:

What is an even number?

Is 834 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 834 is about 28.879.

Thus, the square root of 834 is not an integer, and therefore 834 is not a square number.

What is the square number of 834?

The square of a number (here 834) is the result of the product of this number (834) by itself (i.e., 834 × 834); the square of 834 is sometimes called "raising 834 to the power 2", or "834 squared".

The square of 834 is 695 556 because 834 × 834 = 834² = 695 556.

As a consequence, 834 is the square root of 695 556.

Number of digits of 834

834 is a number with 3 digits.

What are the multiples of 834?

The multiples of 834 are all integers evenly divisible by 834, that is all numbers such that the remainder of the division by 834 is zero. There are infinitely many multiples of 834. The smallest multiples of 834 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 834 too, since 0 × 834 = 0
834: indeed, 834 is a multiple of itself, since 834 is evenly divisible by 834 (we have 834 / 834 = 1, so the remainder of this division is indeed zero)
1 668: indeed, 1 668 = 834 × 2
2 502: indeed, 2 502 = 834 × 3
3 336: indeed, 3 336 = 834 × 4
4 170: indeed, 4 170 = 834 × 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 834). 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 28.879). 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 834

Preceding numbers: …832, 833
Following numbers: 835, 836…

Nearest numbers from 834

Preceding prime number: 829
Following prime number: 839