What are the divisors of 1857?

1, 3, 619, 1857

4 odd divisors

1, 3, 619, 1857

How to compute the divisors of 1857?

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 1857 by each of the numbers from 1 to 1857 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)

  • 1857 / 1 = 1857 (the remainder is 0, so 1 is a divisor of 1857)
  • 1857 / 2 = 928.5 (the remainder is 1, so 2 is not a divisor of 1857)
  • 1857 / 3 = 619 (the remainder is 0, so 3 is a divisor of 1857)
  • ...
  • 1857 / 1856 = 1.0005387931034 (the remainder is 1, so 1856 is not a divisor of 1857)
  • 1857 / 1857 = 1 (the remainder is 0, so 1857 is a divisor of 1857)

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 1857 (i.e. 43.09292285283). 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 )

  • 1857 / 1 = 1857 (the remainder is 0, so 1 and 1857 are divisors of 1857)
  • 1857 / 2 = 928.5 (the remainder is 1, so 2 is not a divisor of 1857)
  • 1857 / 3 = 619 (the remainder is 0, so 3 and 619 are divisors of 1857)
  • ...
  • 1857 / 42 = 44.214285714286 (the remainder is 9, so 42 is not a divisor of 1857)
  • 1857 / 43 = 43.186046511628 (the remainder is 8, so 43 is not a divisor of 1857)