What are the divisors of 1886?

1, 2, 23, 41, 46, 82, 943, 1886

4 even divisors

2, 46, 82, 1886

4 odd divisors

1, 23, 41, 943

How to compute the divisors of 1886?

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 1886 by each of the numbers from 1 to 1886 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)

  • 1886 / 1 = 1886 (the remainder is 0, so 1 is a divisor of 1886)
  • 1886 / 2 = 943 (the remainder is 0, so 2 is a divisor of 1886)
  • 1886 / 3 = 628.66666666667 (the remainder is 2, so 3 is not a divisor of 1886)
  • ...
  • 1886 / 1885 = 1.0005305039788 (the remainder is 1, so 1885 is not a divisor of 1886)
  • 1886 / 1886 = 1 (the remainder is 0, so 1886 is a divisor of 1886)

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 1886 (i.e. 43.428101501217). 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 )

  • 1886 / 1 = 1886 (the remainder is 0, so 1 and 1886 are divisors of 1886)
  • 1886 / 2 = 943 (the remainder is 0, so 2 and 943 are divisors of 1886)
  • 1886 / 3 = 628.66666666667 (the remainder is 2, so 3 is not a divisor of 1886)
  • ...
  • 1886 / 42 = 44.904761904762 (the remainder is 38, so 42 is not a divisor of 1886)
  • 1886 / 43 = 43.860465116279 (the remainder is 37, so 43 is not a divisor of 1886)