Is 391 a prime number? What are the divisors of 391?

Is 391 a prime number?

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

For 391, the answer is: No, 391 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 391) is as follows: 1, 17, 23, 391.

To be 391 a prime number, it would have been required that 391 has only two divisors, i.e., itself and 1.

As a consequence:

  • 391 is a multiple of 1
  • 391 is a multiple of 17
  • 391 is a multiple of 23

To be 391 a prime number, it would have been required that 391 has only two divisors, i.e., itself and 1.

However, 391 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 391 = 17 x 23, where 17 and 23 are both prime numbers.

Is 391 a deficient number?

Yes, 391 is a deficient number, that is to say 391 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 391 without 391 itself (that is 1 + 17 + 23 = 41).

Parity of 391

391 is an odd number, because it is not evenly divisible by 2.

Is 391 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 391 is about 19.774.

Thus, the square root of 391 is not an integer, and therefore 391 is not a square number.

What is the square number of 391?

The square of a number (here 391) is the result of the product of this number (391) by itself (i.e., 391 × 391); the square of 391 is sometimes called "raising 391 to the power 2", or "391 squared".

The square of 391 is 152 881 because 391 × 391 = 3912 = 152 881.

As a consequence, 391 is the square root of 152 881.

Number of digits of 391

391 is a number with 3 digits.

What are the multiples of 391?

The multiples of 391 are all integers evenly divisible by 391, that is all numbers such that the remainder of the division by 391 is zero. There are infinitely many multiples of 391. The smallest multiples of 391 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 391 too, since 0 × 391 = 0
  • 391: indeed, 391 is a multiple of itself, since 391 is evenly divisible by 391 (we have 391 / 391 = 1, so the remainder of this division is indeed zero)
  • 782: indeed, 782 = 391 × 2
  • 1 173: indeed, 1 173 = 391 × 3
  • 1 564: indeed, 1 564 = 391 × 4
  • 1 955: indeed, 1 955 = 391 × 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 391). 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 19.774). 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 391

  • Preceding numbers: …389, 390
  • Following numbers: 392, 393

Nearest numbers from 391

  • Preceding prime number: 389
  • Following prime number: 397
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