What are the divisors of 2292?

1, 2, 3, 4, 6, 12, 191, 382, 573, 764, 1146, 2292

8 even divisors

2, 4, 6, 12, 382, 764, 1146, 2292

4 odd divisors

1, 3, 191, 573

How to compute the divisors of 2292?

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 2292 by each of the numbers from 1 to 2292 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)

  • 2292 / 1 = 2292 (the remainder is 0, so 1 is a divisor of 2292)
  • 2292 / 2 = 1146 (the remainder is 0, so 2 is a divisor of 2292)
  • 2292 / 3 = 764 (the remainder is 0, so 3 is a divisor of 2292)
  • ...
  • 2292 / 2291 = 1.0004364906155 (the remainder is 1, so 2291 is not a divisor of 2292)
  • 2292 / 2292 = 1 (the remainder is 0, so 2292 is a divisor of 2292)

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 2292 (i.e. 47.874836814343). 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 )

  • 2292 / 1 = 2292 (the remainder is 0, so 1 and 2292 are divisors of 2292)
  • 2292 / 2 = 1146 (the remainder is 0, so 2 and 1146 are divisors of 2292)
  • 2292 / 3 = 764 (the remainder is 0, so 3 and 764 are divisors of 2292)
  • ...
  • 2292 / 46 = 49.826086956522 (the remainder is 38, so 46 is not a divisor of 2292)
  • 2292 / 47 = 48.765957446809 (the remainder is 36, so 47 is not a divisor of 2292)