Is 267 a prime number? What are the divisors of 267?

Is 267 a prime number?

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

For 267, the answer is: No, 267 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 267) is as follows: 1, 3, 89, 267.

To be 267 a prime number, it would have been required that 267 has only two divisors, i.e., itself and 1.

As a consequence:

  • 267 is a multiple of 1
  • 267 is a multiple of 3
  • 267 is a multiple of 89

To be 267 a prime number, it would have been required that 267 has only two divisors, i.e., itself and 1.

However, 267 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 267 = 3 x 89, where 3 and 89 are both prime numbers.

Is 267 a deficient number?

Yes, 267 is a deficient number, that is to say 267 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 267 without 267 itself (that is 1 + 3 + 89 = 93).

Parity of 267

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

Is 267 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 267 is about 16.340.

Thus, the square root of 267 is not an integer, and therefore 267 is not a square number.

What is the square number of 267?

The square of a number (here 267) is the result of the product of this number (267) by itself (i.e., 267 × 267); the square of 267 is sometimes called "raising 267 to the power 2", or "267 squared".

The square of 267 is 71 289 because 267 × 267 = 2672 = 71 289.

As a consequence, 267 is the square root of 71 289.

Number of digits of 267

267 is a number with 3 digits.

What are the multiples of 267?

The multiples of 267 are all integers evenly divisible by 267, that is all numbers such that the remainder of the division by 267 is zero. There are infinitely many multiples of 267. The smallest multiples of 267 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 267 too, since 0 × 267 = 0
  • 267: indeed, 267 is a multiple of itself, since 267 is evenly divisible by 267 (we have 267 / 267 = 1, so the remainder of this division is indeed zero)
  • 534: indeed, 534 = 267 × 2
  • 801: indeed, 801 = 267 × 3
  • 1 068: indeed, 1 068 = 267 × 4
  • 1 335: indeed, 1 335 = 267 × 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 267). 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 16.340). 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 267

  • Preceding numbers: …265, 266
  • Following numbers: 268, 269

Nearest numbers from 267

  • Preceding prime number: 263
  • Following prime number: 269
Find out whether some integer is a prime number