Is 361 a prime number? What are the divisors of 361?

Is 361 a prime number?

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

For 361, the answer is: No, 361 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 361) is as follows: 1, 19, 361.

To be 361 a prime number, it would have been required that 361 has only two divisors, i.e., itself and 1.

As a consequence:

  • 361 is a multiple of 1
  • 361 is a multiple of 19

To be 361 a prime number, it would have been required that 361 has only two divisors, i.e., itself and 1.

However, 361 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 361 = 19 x 19, where 19 is a prime number.

Is 361 a deficient number?

Yes, 361 is a deficient number, that is to say 361 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 361 without 361 itself (that is 1 + 19 = 20).

Parity of 361

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

Is 361 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 361 is 19.

Therefore, the square root of 361 is an integer, and as a consequence 361 is a perfect square.

As a consequence, 19 is the square root of 361.

What is the square number of 361?

The square of a number (here 361) is the result of the product of this number (361) by itself (i.e., 361 × 361); the square of 361 is sometimes called "raising 361 to the power 2", or "361 squared".

The square of 361 is 130 321 because 361 × 361 = 3612 = 130 321.

As a consequence, 361 is the square root of 130 321.

Number of digits of 361

361 is a number with 3 digits.

What are the multiples of 361?

The multiples of 361 are all integers evenly divisible by 361, that is all numbers such that the remainder of the division by 361 is zero. There are infinitely many multiples of 361. The smallest multiples of 361 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 361 too, since 0 × 361 = 0
  • 361: indeed, 361 is a multiple of itself, since 361 is evenly divisible by 361 (we have 361 / 361 = 1, so the remainder of this division is indeed zero)
  • 722: indeed, 722 = 361 × 2
  • 1 083: indeed, 1 083 = 361 × 3
  • 1 444: indeed, 1 444 = 361 × 4
  • 1 805: indeed, 1 805 = 361 × 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 361). 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 19). 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 361

  • Preceding numbers: …359, 360
  • Following numbers: 362, 363

Nearest numbers from 361

  • Preceding prime number: 359
  • Following prime number: 367
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