Is 381 a prime number?

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

For 381, the answer is: No, 381 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 381) is as follows: 1, 3, 127, 381.

For 381 to be a prime number, it would have been required that 381 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

381 is a multiple of 1
381 is a multiple of 3
381 is a multiple of 127

For 381 to be a prime number, it would have been required that 381 has only two divisors, i.e., itself and 1.

However, 381 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 381 = 3 x 127, where 3 and 127 are both prime numbers.

Is 381 a deficient number?

Yes, 381 is a deficient number, that is to say 381 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 381 without 381 itself (that is 1 + 3 + 127 = 131).

Parity of 381

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

Find out more:

What is an even number?

Is 381 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 381 is about 19.519.

Thus, the square root of 381 is not an integer, and therefore 381 is not a square number.

What is the square number of 381?

The square of a number (here 381) is the result of the product of this number (381) by itself (i.e., 381 × 381); the square of 381 is sometimes called "raising 381 to the power 2", or "381 squared".

The square of 381 is 145 161 because 381 × 381 = 381² = 145 161.

As a consequence, 381 is the square root of 145 161.

Number of digits of 381

381 is a number with 3 digits.

What are the multiples of 381?

The multiples of 381 are all integers evenly divisible by 381, that is all numbers such that the remainder of the division by 381 is zero. There are infinitely many multiples of 381. The smallest multiples of 381 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 381 too, since 0 × 381 = 0
381: indeed, 381 is a multiple of itself, since 381 is evenly divisible by 381 (we have 381 / 381 = 1, so the remainder of this division is indeed zero)
762: indeed, 762 = 381 × 2
1 143: indeed, 1 143 = 381 × 3
1 524: indeed, 1 524 = 381 × 4
1 905: indeed, 1 905 = 381 × 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 381). 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 19.519). 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 381

Preceding numbers: …379, 380
Following numbers: 382, 383…

Nearest numbers from 381

Preceding prime number: 379
Following prime number: 383