Is 830 a prime number? What are the divisors of 830?

Is 830 a prime number?

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

For 830, the answer is: No, 830 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 830) is as follows: 1, 2, 5, 10, 83, 166, 415, 830.

To be 830 a prime number, it would have been required that 830 has only two divisors, i.e., itself and 1.

As a consequence:

  • 830 is a multiple of 1
  • 830 is a multiple of 2
  • 830 is a multiple of 5
  • 830 is a multiple of 10
  • 830 is a multiple of 83
  • 830 is a multiple of 166
  • 830 is a multiple of 415

To be 830 a prime number, it would have been required that 830 has only two divisors, i.e., itself and 1.

Is 830 a deficient number?

Yes, 830 is a deficient number, that is to say 830 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 830 without 830 itself (that is 1 + 2 + 5 + 10 + 83 + 166 + 415 = 682).

Parity of 830

830 is an even number, because it is evenly divisible by 2: 830 / 2 = 415.

Is 830 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 830 is about 28.810.

Thus, the square root of 830 is not an integer, and therefore 830 is not a square number.

What is the square number of 830?

The square of a number (here 830) is the result of the product of this number (830) by itself (i.e., 830 × 830); the square of 830 is sometimes called "raising 830 to the power 2", or "830 squared".

The square of 830 is 688 900 because 830 × 830 = 8302 = 688 900.

As a consequence, 830 is the square root of 688 900.

Number of digits of 830

830 is a number with 3 digits.

What are the multiples of 830?

The multiples of 830 are all integers evenly divisible by 830, that is all numbers such that the remainder of the division by 830 is zero. There are infinitely many multiples of 830. The smallest multiples of 830 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 830 too, since 0 × 830 = 0
  • 830: indeed, 830 is a multiple of itself, since 830 is evenly divisible by 830 (we have 830 / 830 = 1, so the remainder of this division is indeed zero)
  • 1 660: indeed, 1 660 = 830 × 2
  • 2 490: indeed, 2 490 = 830 × 3
  • 3 320: indeed, 3 320 = 830 × 4
  • 4 150: indeed, 4 150 = 830 × 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 830). 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 28.810). 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 830

  • Preceding numbers: …828, 829
  • Following numbers: 831, 832

Nearest numbers from 830

  • Preceding prime number: 829
  • Following prime number: 839
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