What are the divisors of 9033?

1, 3, 3011, 9033

4 odd divisors

1, 3, 3011, 9033

How to compute the divisors of 9033?

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 9033 by each of the numbers from 1 to 9033 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)

  • 9033 / 1 = 9033 (the remainder is 0, so 1 is a divisor of 9033)
  • 9033 / 2 = 4516.5 (the remainder is 1, so 2 is not a divisor of 9033)
  • 9033 / 3 = 3011 (the remainder is 0, so 3 is a divisor of 9033)
  • ...
  • 9033 / 9032 = 1.0001107174491 (the remainder is 1, so 9032 is not a divisor of 9033)
  • 9033 / 9033 = 1 (the remainder is 0, so 9033 is a divisor of 9033)

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 9033 (i.e. 95.042095936485). 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 )

  • 9033 / 1 = 9033 (the remainder is 0, so 1 and 9033 are divisors of 9033)
  • 9033 / 2 = 4516.5 (the remainder is 1, so 2 is not a divisor of 9033)
  • 9033 / 3 = 3011 (the remainder is 0, so 3 and 3011 are divisors of 9033)
  • ...
  • 9033 / 94 = 96.095744680851 (the remainder is 9, so 94 is not a divisor of 9033)
  • 9033 / 95 = 95.084210526316 (the remainder is 8, so 95 is not a divisor of 9033)