Is 392 a prime number?

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

For 392, the answer is: No, 392 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 392) is as follows: 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.

For 392 to be a prime number, it would have been required that 392 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

392 is a multiple of 1
392 is a multiple of 2
392 is a multiple of 4
392 is a multiple of 7
392 is a multiple of 8
392 is a multiple of 14
392 is a multiple of 28
392 is a multiple of 49
392 is a multiple of 56
392 is a multiple of 98
392 is a multiple of 196

For 392 to be a prime number, it would have been required that 392 has only two divisors, i.e., itself and 1.

Is 392 a deficient number?

No, 392 is not a deficient number: to be deficient, 392 should have been such that 392 is larger than the sum of its proper divisors, i.e., the divisors of 392 without 392 itself (that is 1 + 2 + 4 + 7 + 8 + 14 + 28 + 49 + 56 + 98 + 196 = 463).

In fact, 392 is an abundant number; 392 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 8 + 14 + 28 + 49 + 56 + 98 + 196 = 463). The smallest abundant number is 12.

Parity of 392

392 is an even number, because it is evenly divisible by 2: 392 / 2 = 196.

Find out more:

What is an even number?

Is 392 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 392 is about 19.799.

Thus, the square root of 392 is not an integer, and therefore 392 is not a square number.

What is the square number of 392?

The square of a number (here 392) is the result of the product of this number (392) by itself (i.e., 392 × 392); the square of 392 is sometimes called "raising 392 to the power 2", or "392 squared".

The square of 392 is 153 664 because 392 × 392 = 392² = 153 664.

As a consequence, 392 is the square root of 153 664.

Number of digits of 392

392 is a number with 3 digits.

What are the multiples of 392?

The multiples of 392 are all integers evenly divisible by 392, that is all numbers such that the remainder of the division by 392 is zero. There are infinitely many multiples of 392. The smallest multiples of 392 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 392 too, since 0 × 392 = 0
392: indeed, 392 is a multiple of itself, since 392 is evenly divisible by 392 (we have 392 / 392 = 1, so the remainder of this division is indeed zero)
784: indeed, 784 = 392 × 2
1 176: indeed, 1 176 = 392 × 3
1 568: indeed, 1 568 = 392 × 4
1 960: indeed, 1 960 = 392 × 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 392). 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 19.799). 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 392

Preceding numbers: …390, 391
Following numbers: 393, 394…

Nearest numbers from 392

Preceding prime number: 389
Following prime number: 397