What are the divisors of 866?

1, 2, 433, 866

2 even divisors

2, 866

2 odd divisors

1, 433

How to compute the divisors of 866?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

N mod M = 0

Brute force algorithm

We could start by using a brute-force method which would involve dividing 866 by each of the numbers from 1 to 866 to determine which ones have a remainder equal to 0.

Remainder = N ( M × N M )

(where N M is the integer part of the quotient)

  • 866 / 1 = 866 (the remainder is 0, so 1 is a divisor of 866)
  • 866 / 2 = 433 (the remainder is 0, so 2 is a divisor of 866)
  • 866 / 3 = 288.66666666667 (the remainder is 2, so 3 is not a divisor of 866)
  • ...
  • 866 / 865 = 1.0011560693642 (the remainder is 1, so 865 is not a divisor of 866)
  • 866 / 866 = 1 (the remainder is 0, so 866 is a divisor of 866)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 866 (i.e. 29.427877939124). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

D × d = N

(thus, if N D = d , then N d = D )

  • 866 / 1 = 866 (the remainder is 0, so 1 and 866 are divisors of 866)
  • 866 / 2 = 433 (the remainder is 0, so 2 and 433 are divisors of 866)
  • 866 / 3 = 288.66666666667 (the remainder is 2, so 3 is not a divisor of 866)
  • ...
  • 866 / 28 = 30.928571428571 (the remainder is 26, so 28 is not a divisor of 866)
  • 866 / 29 = 29.862068965517 (the remainder is 25, so 29 is not a divisor of 866)