What are the divisors of 9603?

1, 3, 9, 11, 33, 97, 99, 291, 873, 1067, 3201, 9603

12 odd divisors

1, 3, 9, 11, 33, 97, 99, 291, 873, 1067, 3201, 9603

How to compute the divisors of 9603?

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 9603 by each of the numbers from 1 to 9603 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)

  • 9603 / 1 = 9603 (the remainder is 0, so 1 is a divisor of 9603)
  • 9603 / 2 = 4801.5 (the remainder is 1, so 2 is not a divisor of 9603)
  • 9603 / 3 = 3201 (the remainder is 0, so 3 is a divisor of 9603)
  • ...
  • 9603 / 9602 = 1.0001041449698 (the remainder is 1, so 9602 is not a divisor of 9603)
  • 9603 / 9603 = 1 (the remainder is 0, so 9603 is a divisor of 9603)

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 9603 (i.e. 97.994897826366). 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 )

  • 9603 / 1 = 9603 (the remainder is 0, so 1 and 9603 are divisors of 9603)
  • 9603 / 2 = 4801.5 (the remainder is 1, so 2 is not a divisor of 9603)
  • 9603 / 3 = 3201 (the remainder is 0, so 3 and 3201 are divisors of 9603)
  • ...
  • 9603 / 96 = 100.03125 (the remainder is 3, so 96 is not a divisor of 9603)
  • 9603 / 97 = 99 (the remainder is 0, so 97 and 99 are divisors of 9603)