Is 824 a prime number? What are the divisors of 824?

Is 824 a prime number?

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

For 824, the answer is: No, 824 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 824) is as follows: 1, 2, 4, 8, 103, 206, 412, 824.

To be 824 a prime number, it would have been required that 824 has only two divisors, i.e., itself and 1.

As a consequence:

  • 824 is a multiple of 1
  • 824 is a multiple of 2
  • 824 is a multiple of 4
  • 824 is a multiple of 8
  • 824 is a multiple of 103
  • 824 is a multiple of 206
  • 824 is a multiple of 412

To be 824 a prime number, it would have been required that 824 has only two divisors, i.e., itself and 1.

Is 824 a deficient number?

Yes, 824 is a deficient number, that is to say 824 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 824 without 824 itself (that is 1 + 2 + 4 + 8 + 103 + 206 + 412 = 736).

Parity of 824

824 is an even number, because it is evenly divisible by 2: 824 / 2 = 412.

Is 824 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 824 is about 28.705.

Thus, the square root of 824 is not an integer, and therefore 824 is not a square number.

What is the square number of 824?

The square of a number (here 824) is the result of the product of this number (824) by itself (i.e., 824 × 824); the square of 824 is sometimes called "raising 824 to the power 2", or "824 squared".

The square of 824 is 678 976 because 824 × 824 = 8242 = 678 976.

As a consequence, 824 is the square root of 678 976.

Number of digits of 824

824 is a number with 3 digits.

What are the multiples of 824?

The multiples of 824 are all integers evenly divisible by 824, that is all numbers such that the remainder of the division by 824 is zero. There are infinitely many multiples of 824. The smallest multiples of 824 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 824 too, since 0 × 824 = 0
  • 824: indeed, 824 is a multiple of itself, since 824 is evenly divisible by 824 (we have 824 / 824 = 1, so the remainder of this division is indeed zero)
  • 1 648: indeed, 1 648 = 824 × 2
  • 2 472: indeed, 2 472 = 824 × 3
  • 3 296: indeed, 3 296 = 824 × 4
  • 4 120: indeed, 4 120 = 824 × 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 824). 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 28.705). 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 824

  • Preceding numbers: …822, 823
  • Following numbers: 825, 826

Nearest numbers from 824

  • Preceding prime number: 823
  • Following prime number: 827
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