What are the divisors of 2851?

1, 2851

2 odd divisors

1, 2851

How to compute the divisors of 2851?

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 2851 by each of the numbers from 1 to 2851 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)

  • 2851 / 1 = 2851 (the remainder is 0, so 1 is a divisor of 2851)
  • 2851 / 2 = 1425.5 (the remainder is 1, so 2 is not a divisor of 2851)
  • 2851 / 3 = 950.33333333333 (the remainder is 1, so 3 is not a divisor of 2851)
  • ...
  • 2851 / 2850 = 1.000350877193 (the remainder is 1, so 2850 is not a divisor of 2851)
  • 2851 / 2851 = 1 (the remainder is 0, so 2851 is a divisor of 2851)

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 2851 (i.e. 53.39475629685). 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 )

  • 2851 / 1 = 2851 (the remainder is 0, so 1 and 2851 are divisors of 2851)
  • 2851 / 2 = 1425.5 (the remainder is 1, so 2 is not a divisor of 2851)
  • 2851 / 3 = 950.33333333333 (the remainder is 1, so 3 is not a divisor of 2851)
  • ...
  • 2851 / 52 = 54.826923076923 (the remainder is 43, so 52 is not a divisor of 2851)
  • 2851 / 53 = 53.792452830189 (the remainder is 42, so 53 is not a divisor of 2851)