Is 867 a prime number? What are the divisors of 867?

Is 867 a prime number?

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

For 867, the answer is: No, 867 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 867) is as follows: 1, 3, 17, 51, 289, 867.

To be 867 a prime number, it would have been required that 867 has only two divisors, i.e., itself and 1.

As a consequence:

  • 867 is a multiple of 1
  • 867 is a multiple of 3
  • 867 is a multiple of 17
  • 867 is a multiple of 51
  • 867 is a multiple of 289

To be 867 a prime number, it would have been required that 867 has only two divisors, i.e., itself and 1.

Is 867 a deficient number?

Yes, 867 is a deficient number, that is to say 867 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 867 without 867 itself (that is 1 + 3 + 17 + 51 + 289 = 361).

Parity of 867

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

Is 867 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 867 is about 29.445.

Thus, the square root of 867 is not an integer, and therefore 867 is not a square number.

What is the square number of 867?

The square of a number (here 867) is the result of the product of this number (867) by itself (i.e., 867 × 867); the square of 867 is sometimes called "raising 867 to the power 2", or "867 squared".

The square of 867 is 751 689 because 867 × 867 = 8672 = 751 689.

As a consequence, 867 is the square root of 751 689.

Number of digits of 867

867 is a number with 3 digits.

What are the multiples of 867?

The multiples of 867 are all integers evenly divisible by 867, that is all numbers such that the remainder of the division by 867 is zero. There are infinitely many multiples of 867. The smallest multiples of 867 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 867 too, since 0 × 867 = 0
  • 867: indeed, 867 is a multiple of itself, since 867 is evenly divisible by 867 (we have 867 / 867 = 1, so the remainder of this division is indeed zero)
  • 1 734: indeed, 1 734 = 867 × 2
  • 2 601: indeed, 2 601 = 867 × 3
  • 3 468: indeed, 3 468 = 867 × 4
  • 4 335: indeed, 4 335 = 867 × 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 867). 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 29.445). 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 867

  • Preceding numbers: …865, 866
  • Following numbers: 868, 869

Nearest numbers from 867

  • Preceding prime number: 863
  • Following prime number: 877
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