Is 360 a prime number? What are the divisors of 360?

Is 360 a prime number?

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

For 360, the answer is: No, 360 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 360) is as follows: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.

To be 360 a prime number, it would have been required that 360 has only two divisors, i.e., itself and 1.

As a consequence:

  • 360 is a multiple of 1
  • 360 is a multiple of 2
  • 360 is a multiple of 3
  • 360 is a multiple of 4
  • 360 is a multiple of 5
  • 360 is a multiple of 6
  • 360 is a multiple of 8
  • 360 is a multiple of 9
  • 360 is a multiple of 10
  • 360 is a multiple of 12
  • 360 is a multiple of 15
  • 360 is a multiple of 18
  • 360 is a multiple of 20
  • 360 is a multiple of 24
  • 360 is a multiple of 30
  • 360 is a multiple of 36
  • 360 is a multiple of 40
  • 360 is a multiple of 45
  • 360 is a multiple of 60
  • 360 is a multiple of 72
  • 360 is a multiple of 90
  • 360 is a multiple of 120
  • 360 is a multiple of 180

To be 360 a prime number, it would have been required that 360 has only two divisors, i.e., itself and 1.

Is 360 a deficient number?

No, 360 is not a deficient number: to be deficient, 360 should have been such that 360 is larger than the sum of its proper divisors, i.e., the divisors of 360 without 360 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 60 + 72 + 90 + 120 + 180 = 810).

In fact, 360 is an abundant number; 360 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 60 + 72 + 90 + 120 + 180 = 810). The smallest abundant number is 12.

Parity of 360

360 is an even number, because it is evenly divisible by 2: 360 / 2 = 180.

Is 360 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 360 is about 18.974.

Thus, the square root of 360 is not an integer, and therefore 360 is not a square number.

What is the square number of 360?

The square of a number (here 360) is the result of the product of this number (360) by itself (i.e., 360 × 360); the square of 360 is sometimes called "raising 360 to the power 2", or "360 squared".

The square of 360 is 129 600 because 360 × 360 = 3602 = 129 600.

As a consequence, 360 is the square root of 129 600.

Number of digits of 360

360 is a number with 3 digits.

What are the multiples of 360?

The multiples of 360 are all integers evenly divisible by 360, that is all numbers such that the remainder of the division by 360 is zero. There are infinitely many multiples of 360. The smallest multiples of 360 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 360 too, since 0 × 360 = 0
  • 360: indeed, 360 is a multiple of itself, since 360 is evenly divisible by 360 (we have 360 / 360 = 1, so the remainder of this division is indeed zero)
  • 720: indeed, 720 = 360 × 2
  • 1 080: indeed, 1 080 = 360 × 3
  • 1 440: indeed, 1 440 = 360 × 4
  • 1 800: indeed, 1 800 = 360 × 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 360). 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 18.974). 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 360

  • Preceding numbers: …358, 359
  • Following numbers: 361, 362

Nearest numbers from 360

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