Is 268 a prime number? What are the divisors of 268?

Is 268 a prime number?

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

For 268, the answer is: No, 268 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 268) is as follows: 1, 2, 4, 67, 134, 268.

To be 268 a prime number, it would have been required that 268 has only two divisors, i.e., itself and 1.

As a consequence:

  • 268 is a multiple of 1
  • 268 is a multiple of 2
  • 268 is a multiple of 4
  • 268 is a multiple of 67
  • 268 is a multiple of 134

To be 268 a prime number, it would have been required that 268 has only two divisors, i.e., itself and 1.

Is 268 a deficient number?

Yes, 268 is a deficient number, that is to say 268 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 268 without 268 itself (that is 1 + 2 + 4 + 67 + 134 = 208).

Parity of 268

268 is an even number, because it is evenly divisible by 2: 268 / 2 = 134.

Is 268 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 268 is about 16.371.

Thus, the square root of 268 is not an integer, and therefore 268 is not a square number.

What is the square number of 268?

The square of a number (here 268) is the result of the product of this number (268) by itself (i.e., 268 × 268); the square of 268 is sometimes called "raising 268 to the power 2", or "268 squared".

The square of 268 is 71 824 because 268 × 268 = 2682 = 71 824.

As a consequence, 268 is the square root of 71 824.

Number of digits of 268

268 is a number with 3 digits.

What are the multiples of 268?

The multiples of 268 are all integers evenly divisible by 268, that is all numbers such that the remainder of the division by 268 is zero. There are infinitely many multiples of 268. The smallest multiples of 268 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 268 too, since 0 × 268 = 0
  • 268: indeed, 268 is a multiple of itself, since 268 is evenly divisible by 268 (we have 268 / 268 = 1, so the remainder of this division is indeed zero)
  • 536: indeed, 536 = 268 × 2
  • 804: indeed, 804 = 268 × 3
  • 1 072: indeed, 1 072 = 268 × 4
  • 1 340: indeed, 1 340 = 268 × 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 268). 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 16.371). 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 268

  • Preceding numbers: …266, 267
  • Following numbers: 269, 270

Nearest numbers from 268

  • Preceding prime number: 263
  • Following prime number: 269
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