Is 371 a prime number? What are the divisors of 371?

Is 371 a prime number?

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

For 371, the answer is: No, 371 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 371) is as follows: 1, 7, 53, 371.

To be 371 a prime number, it would have been required that 371 has only two divisors, i.e., itself and 1.

As a consequence:

  • 371 is a multiple of 1
  • 371 is a multiple of 7
  • 371 is a multiple of 53

To be 371 a prime number, it would have been required that 371 has only two divisors, i.e., itself and 1.

However, 371 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 371 = 7 x 53, where 7 and 53 are both prime numbers.

Is 371 a deficient number?

Yes, 371 is a deficient number, that is to say 371 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 371 without 371 itself (that is 1 + 7 + 53 = 61).

Parity of 371

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

Is 371 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 371 is about 19.261.

Thus, the square root of 371 is not an integer, and therefore 371 is not a square number.

What is the square number of 371?

The square of a number (here 371) is the result of the product of this number (371) by itself (i.e., 371 × 371); the square of 371 is sometimes called "raising 371 to the power 2", or "371 squared".

The square of 371 is 137 641 because 371 × 371 = 3712 = 137 641.

As a consequence, 371 is the square root of 137 641.

Number of digits of 371

371 is a number with 3 digits.

What are the multiples of 371?

The multiples of 371 are all integers evenly divisible by 371, that is all numbers such that the remainder of the division by 371 is zero. There are infinitely many multiples of 371. The smallest multiples of 371 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 371 too, since 0 × 371 = 0
  • 371: indeed, 371 is a multiple of itself, since 371 is evenly divisible by 371 (we have 371 / 371 = 1, so the remainder of this division is indeed zero)
  • 742: indeed, 742 = 371 × 2
  • 1 113: indeed, 1 113 = 371 × 3
  • 1 484: indeed, 1 484 = 371 × 4
  • 1 855: indeed, 1 855 = 371 × 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 371). 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 19.261). 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 371

  • Preceding numbers: …369, 370
  • Following numbers: 372, 373

Nearest numbers from 371

  • Preceding prime number: 367
  • Following prime number: 373
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