Is 384 a prime number?

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

For 384, the answer is: No, 384 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 384) is as follows: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.

For 384 to be a prime number, it would have been required that 384 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

384 is a multiple of 1
384 is a multiple of 2
384 is a multiple of 3
384 is a multiple of 4
384 is a multiple of 6
384 is a multiple of 8
384 is a multiple of 12
384 is a multiple of 16
384 is a multiple of 24
384 is a multiple of 32
384 is a multiple of 48
384 is a multiple of 64
384 is a multiple of 96
384 is a multiple of 128
384 is a multiple of 192

For 384 to be a prime number, it would have been required that 384 has only two divisors, i.e., itself and 1.

Is 384 a deficient number?

No, 384 is not a deficient number: to be deficient, 384 should have been such that 384 is larger than the sum of its proper divisors, i.e., the divisors of 384 without 384 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 = 636).

In fact, 384 is an abundant number; 384 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 64 + 96 + 128 + 192 = 636). The smallest abundant number is 12.

Parity of 384

384 is an even number, because it is evenly divisible by 2: 384 / 2 = 192.

Find out more:

What is an even number?

Is 384 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 384 is about 19.596.

Thus, the square root of 384 is not an integer, and therefore 384 is not a square number.

What is the square number of 384?

The square of a number (here 384) is the result of the product of this number (384) by itself (i.e., 384 × 384); the square of 384 is sometimes called "raising 384 to the power 2", or "384 squared".

The square of 384 is 147 456 because 384 × 384 = 384² = 147 456.

As a consequence, 384 is the square root of 147 456.

Number of digits of 384

384 is a number with 3 digits.

What are the multiples of 384?

The multiples of 384 are all integers evenly divisible by 384, that is all numbers such that the remainder of the division by 384 is zero. There are infinitely many multiples of 384. The smallest multiples of 384 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 384 too, since 0 × 384 = 0
384: indeed, 384 is a multiple of itself, since 384 is evenly divisible by 384 (we have 384 / 384 = 1, so the remainder of this division is indeed zero)
768: indeed, 768 = 384 × 2
1 152: indeed, 1 152 = 384 × 3
1 536: indeed, 1 536 = 384 × 4
1 920: indeed, 1 920 = 384 × 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 384). 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 19.596). 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 384

Preceding numbers: …382, 383
Following numbers: 385, 386…

Nearest numbers from 384

Preceding prime number: 383
Following prime number: 389