Is 304 a prime number? What are the divisors of 304?

Is 304 a prime number?

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

For 304, the answer is: No, 304 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 304) is as follows: 1, 2, 4, 8, 16, 19, 38, 76, 152, 304.

To be 304 a prime number, it would have been required that 304 has only two divisors, i.e., itself and 1.

As a consequence:

  • 304 is a multiple of 1
  • 304 is a multiple of 2
  • 304 is a multiple of 4
  • 304 is a multiple of 8
  • 304 is a multiple of 16
  • 304 is a multiple of 19
  • 304 is a multiple of 38
  • 304 is a multiple of 76
  • 304 is a multiple of 152

To be 304 a prime number, it would have been required that 304 has only two divisors, i.e., itself and 1.

Is 304 a deficient number?

No, 304 is not a deficient number: to be deficient, 304 should have been such that 304 is larger than the sum of its proper divisors, i.e., the divisors of 304 without 304 itself (that is 1 + 2 + 4 + 8 + 16 + 19 + 38 + 76 + 152 = 316).

In fact, 304 is an abundant number; 304 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 16 + 19 + 38 + 76 + 152 = 316). The smallest abundant number is 12.

Parity of 304

304 is an even number, because it is evenly divisible by 2: 304 / 2 = 152.

Is 304 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 304 is about 17.436.

Thus, the square root of 304 is not an integer, and therefore 304 is not a square number.

What is the square number of 304?

The square of a number (here 304) is the result of the product of this number (304) by itself (i.e., 304 × 304); the square of 304 is sometimes called "raising 304 to the power 2", or "304 squared".

The square of 304 is 92 416 because 304 × 304 = 3042 = 92 416.

As a consequence, 304 is the square root of 92 416.

Number of digits of 304

304 is a number with 3 digits.

What are the multiples of 304?

The multiples of 304 are all integers evenly divisible by 304, that is all numbers such that the remainder of the division by 304 is zero. There are infinitely many multiples of 304. The smallest multiples of 304 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 304 too, since 0 × 304 = 0
  • 304: indeed, 304 is a multiple of itself, since 304 is evenly divisible by 304 (we have 304 / 304 = 1, so the remainder of this division is indeed zero)
  • 608: indeed, 608 = 304 × 2
  • 912: indeed, 912 = 304 × 3
  • 1 216: indeed, 1 216 = 304 × 4
  • 1 520: indeed, 1 520 = 304 × 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 304). 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 17.436). 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 304

  • Preceding numbers: …302, 303
  • Following numbers: 305, 306

Nearest numbers from 304

  • Preceding prime number: 293
  • Following prime number: 307
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