Is 841 a prime number? What are the divisors of 841?

Is 841 a prime number?

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

For 841, the answer is: No, 841 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 841) is as follows: 1, 29, 841.

To be 841 a prime number, it would have been required that 841 has only two divisors, i.e., itself and 1.

As a consequence:

  • 841 is a multiple of 1
  • 841 is a multiple of 29

To be 841 a prime number, it would have been required that 841 has only two divisors, i.e., itself and 1.

However, 841 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 841 = 29 x 29, where 29 is a prime number.

Is 841 a deficient number?

Yes, 841 is a deficient number, that is to say 841 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 841 without 841 itself (that is 1 + 29 = 30).

Parity of 841

841 is an odd number, because it is not evenly divisible by 2.

Is 841 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 841 is 29.

Therefore, the square root of 841 is an integer, and as a consequence 841 is a perfect square.

As a consequence, 29 is the square root of 841.

What is the square number of 841?

The square of a number (here 841) is the result of the product of this number (841) by itself (i.e., 841 × 841); the square of 841 is sometimes called "raising 841 to the power 2", or "841 squared".

The square of 841 is 707 281 because 841 × 841 = 8412 = 707 281.

As a consequence, 841 is the square root of 707 281.

Number of digits of 841

841 is a number with 3 digits.

What are the multiples of 841?

The multiples of 841 are all integers evenly divisible by 841, that is all numbers such that the remainder of the division by 841 is zero. There are infinitely many multiples of 841. The smallest multiples of 841 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 841 too, since 0 × 841 = 0
  • 841: indeed, 841 is a multiple of itself, since 841 is evenly divisible by 841 (we have 841 / 841 = 1, so the remainder of this division is indeed zero)
  • 1 682: indeed, 1 682 = 841 × 2
  • 2 523: indeed, 2 523 = 841 × 3
  • 3 364: indeed, 3 364 = 841 × 4
  • 4 205: indeed, 4 205 = 841 × 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 841). 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 29). 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 841

  • Preceding numbers: …839, 840
  • Following numbers: 842, 843

Nearest numbers from 841

  • Preceding prime number: 839
  • Following prime number: 853
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