Is 380 a prime number?

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

For 380, the answer is: No, 380 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 380) is as follows: 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380.

For 380 to be a prime number, it would have been required that 380 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 380 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 380 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

380 is a multiple of 1
380 is a multiple of 2
380 is a multiple of 4
380 is a multiple of 5
380 is a multiple of 10
380 is a multiple of 19
380 is a multiple of 20
380 is a multiple of 38
380 is a multiple of 76
380 is a multiple of 95
380 is a multiple of 190

For 380 to be a prime number, it would have been required that 380 has only two divisors, i.e., itself and 1.

Is 380 a deficient number?

No, 380 is not a deficient number: to be deficient, 380 should have been such that 380 is larger than the sum of its proper divisors, i.e., the divisors of 380 without 380 itself (that is 1 + 2 + 4 + 5 + 10 + 19 + 20 + 38 + 76 + 95 + 190 = 460).

In fact, 380 is an abundant number; 380 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 + 19 + 20 + 38 + 76 + 95 + 190 = 460). The smallest abundant number is 12.

Parity of 380

380 is an even number, because it is evenly divisible by 2: 380 / 2 = 190.

Find out more:

What is an even number?

Is 380 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 380 is about 19.494.

Thus, the square root of 380 is not an integer, and therefore 380 is not a square number.

What is the square number of 380?

The square of a number (here 380) is the result of the product of this number (380) by itself (i.e., 380 × 380); the square of 380 is sometimes called "raising 380 to the power 2", or "380 squared".

The square of 380 is 144 400 because 380 × 380 = 380² = 144 400.

As a consequence, 380 is the square root of 144 400.

Number of digits of 380

380 is a number with 3 digits.

What are the multiples of 380?

The multiples of 380 are all integers evenly divisible by 380, that is all numbers such that the remainder of the division by 380 is zero. There are infinitely many multiples of 380. The smallest multiples of 380 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 380 too, since 0 × 380 = 0
380: indeed, 380 is a multiple of itself, since 380 is evenly divisible by 380 (we have 380 / 380 = 1, so the remainder of this division is indeed zero)
760: indeed, 760 = 380 × 2
1 140: indeed, 1 140 = 380 × 3
1 520: indeed, 1 520 = 380 × 4
1 900: indeed, 1 900 = 380 × 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 380). 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 19.494). 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 380

Preceding numbers: …378, 379
Following numbers: 381, 382…

Nearest numbers from 380

Preceding prime number: 379
Following prime number: 383