What are the divisors of 4569?

1, 3, 1523, 4569

4 odd divisors

1, 3, 1523, 4569

How to compute the divisors of 4569?

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 4569 by each of the numbers from 1 to 4569 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)

  • 4569 / 1 = 4569 (the remainder is 0, so 1 is a divisor of 4569)
  • 4569 / 2 = 2284.5 (the remainder is 1, so 2 is not a divisor of 4569)
  • 4569 / 3 = 1523 (the remainder is 0, so 3 is a divisor of 4569)
  • ...
  • 4569 / 4568 = 1.0002189141856 (the remainder is 1, so 4568 is not a divisor of 4569)
  • 4569 / 4569 = 1 (the remainder is 0, so 4569 is a divisor of 4569)

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 4569 (i.e. 67.594378464485). 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 )

  • 4569 / 1 = 4569 (the remainder is 0, so 1 and 4569 are divisors of 4569)
  • 4569 / 2 = 2284.5 (the remainder is 1, so 2 is not a divisor of 4569)
  • 4569 / 3 = 1523 (the remainder is 0, so 3 and 1523 are divisors of 4569)
  • ...
  • 4569 / 66 = 69.227272727273 (the remainder is 15, so 66 is not a divisor of 4569)
  • 4569 / 67 = 68.194029850746 (the remainder is 13, so 67 is not a divisor of 4569)