Is 363 a prime number? What are the divisors of 363?

Is 363 a prime number?

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

For 363, the answer is: No, 363 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 363) is as follows: 1, 3, 11, 33, 121, 363.

To be 363 a prime number, it would have been required that 363 has only two divisors, i.e., itself and 1.

As a consequence:

  • 363 is a multiple of 1
  • 363 is a multiple of 3
  • 363 is a multiple of 11
  • 363 is a multiple of 33
  • 363 is a multiple of 121

To be 363 a prime number, it would have been required that 363 has only two divisors, i.e., itself and 1.

Is 363 a deficient number?

Yes, 363 is a deficient number, that is to say 363 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 363 without 363 itself (that is 1 + 3 + 11 + 33 + 121 = 169).

Parity of 363

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

Is 363 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 363 is about 19.053.

Thus, the square root of 363 is not an integer, and therefore 363 is not a square number.

What is the square number of 363?

The square of a number (here 363) is the result of the product of this number (363) by itself (i.e., 363 × 363); the square of 363 is sometimes called "raising 363 to the power 2", or "363 squared".

The square of 363 is 131 769 because 363 × 363 = 3632 = 131 769.

As a consequence, 363 is the square root of 131 769.

Number of digits of 363

363 is a number with 3 digits.

What are the multiples of 363?

The multiples of 363 are all integers evenly divisible by 363, that is all numbers such that the remainder of the division by 363 is zero. There are infinitely many multiples of 363. The smallest multiples of 363 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 363 too, since 0 × 363 = 0
  • 363: indeed, 363 is a multiple of itself, since 363 is evenly divisible by 363 (we have 363 / 363 = 1, so the remainder of this division is indeed zero)
  • 726: indeed, 726 = 363 × 2
  • 1 089: indeed, 1 089 = 363 × 3
  • 1 452: indeed, 1 452 = 363 × 4
  • 1 815: indeed, 1 815 = 363 × 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 363). 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 19.053). 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 363

  • Preceding numbers: …361, 362
  • Following numbers: 364, 365

Nearest numbers from 363

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