Is 270 a prime number? What are the divisors of 270?

Is 270 a prime number?

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

For 270, the answer is: No, 270 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 270) is as follows: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.

To be 270 a prime number, it would have been required that 270 has only two divisors, i.e., itself and 1.

As a consequence:

  • 270 is a multiple of 1
  • 270 is a multiple of 2
  • 270 is a multiple of 3
  • 270 is a multiple of 5
  • 270 is a multiple of 6
  • 270 is a multiple of 9
  • 270 is a multiple of 10
  • 270 is a multiple of 15
  • 270 is a multiple of 18
  • 270 is a multiple of 27
  • 270 is a multiple of 30
  • 270 is a multiple of 45
  • 270 is a multiple of 54
  • 270 is a multiple of 90
  • 270 is a multiple of 135

To be 270 a prime number, it would have been required that 270 has only two divisors, i.e., itself and 1.

Is 270 a deficient number?

No, 270 is not a deficient number: to be deficient, 270 should have been such that 270 is larger than the sum of its proper divisors, i.e., the divisors of 270 without 270 itself (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 = 450).

In fact, 270 is an abundant number; 270 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 = 450). The smallest abundant number is 12.

Parity of 270

270 is an even number, because it is evenly divisible by 2: 270 / 2 = 135.

Is 270 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 270 is about 16.432.

Thus, the square root of 270 is not an integer, and therefore 270 is not a square number.

What is the square number of 270?

The square of a number (here 270) is the result of the product of this number (270) by itself (i.e., 270 × 270); the square of 270 is sometimes called "raising 270 to the power 2", or "270 squared".

The square of 270 is 72 900 because 270 × 270 = 2702 = 72 900.

As a consequence, 270 is the square root of 72 900.

Number of digits of 270

270 is a number with 3 digits.

What are the multiples of 270?

The multiples of 270 are all integers evenly divisible by 270, that is all numbers such that the remainder of the division by 270 is zero. There are infinitely many multiples of 270. The smallest multiples of 270 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 270 too, since 0 × 270 = 0
  • 270: indeed, 270 is a multiple of itself, since 270 is evenly divisible by 270 (we have 270 / 270 = 1, so the remainder of this division is indeed zero)
  • 540: indeed, 540 = 270 × 2
  • 810: indeed, 810 = 270 × 3
  • 1 080: indeed, 1 080 = 270 × 4
  • 1 350: indeed, 1 350 = 270 × 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 270). 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 16.432). 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 270

  • Preceding numbers: …268, 269
  • Following numbers: 271, 272

Nearest numbers from 270

  • Preceding prime number: 269
  • Following prime number: 271
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