Is 390 a prime number?

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

For 390, the answer is: No, 390 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 390) is as follows: 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.

For 390 to be a prime number, it would have been required that 390 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 390 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 390 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

390 is a multiple of 1
390 is a multiple of 2
390 is a multiple of 3
390 is a multiple of 5
390 is a multiple of 6
390 is a multiple of 10
390 is a multiple of 13
390 is a multiple of 15
390 is a multiple of 26
390 is a multiple of 30
390 is a multiple of 39
390 is a multiple of 65
390 is a multiple of 78
390 is a multiple of 130
390 is a multiple of 195

For 390 to be a prime number, it would have been required that 390 has only two divisors, i.e., itself and 1.

Is 390 a deficient number?

No, 390 is not a deficient number: to be deficient, 390 should have been such that 390 is larger than the sum of its proper divisors, i.e., the divisors of 390 without 390 itself (that is 1 + 2 + 3 + 5 + 6 + 10 + 13 + 15 + 26 + 30 + 39 + 65 + 78 + 130 + 195 = 618).

In fact, 390 is an abundant number; 390 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 10 + 13 + 15 + 26 + 30 + 39 + 65 + 78 + 130 + 195 = 618). The smallest abundant number is 12.

Parity of 390

390 is an even number, because it is evenly divisible by 2: 390 / 2 = 195.

Find out more:

What is an even number?

Is 390 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 390 is about 19.748.

Thus, the square root of 390 is not an integer, and therefore 390 is not a square number.

What is the square number of 390?

The square of a number (here 390) is the result of the product of this number (390) by itself (i.e., 390 × 390); the square of 390 is sometimes called "raising 390 to the power 2", or "390 squared".

The square of 390 is 152 100 because 390 × 390 = 390² = 152 100.

As a consequence, 390 is the square root of 152 100.

Number of digits of 390

390 is a number with 3 digits.

What are the multiples of 390?

The multiples of 390 are all integers evenly divisible by 390, that is all numbers such that the remainder of the division by 390 is zero. There are infinitely many multiples of 390. The smallest multiples of 390 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 390 too, since 0 × 390 = 0
390: indeed, 390 is a multiple of itself, since 390 is evenly divisible by 390 (we have 390 / 390 = 1, so the remainder of this division is indeed zero)
780: indeed, 780 = 390 × 2
1 170: indeed, 1 170 = 390 × 3
1 560: indeed, 1 560 = 390 × 4
1 950: indeed, 1 950 = 390 × 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 390). 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 19.748). 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 390

Preceding numbers: …388, 389
Following numbers: 391, 392…

Nearest numbers from 390

Preceding prime number: 389
Following prime number: 397