What are the divisors of 4175?

1, 5, 25, 167, 835, 4175

6 odd divisors

1, 5, 25, 167, 835, 4175

How to compute the divisors of 4175?

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 4175 by each of the numbers from 1 to 4175 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)

  • 4175 / 1 = 4175 (the remainder is 0, so 1 is a divisor of 4175)
  • 4175 / 2 = 2087.5 (the remainder is 1, so 2 is not a divisor of 4175)
  • 4175 / 3 = 1391.6666666667 (the remainder is 2, so 3 is not a divisor of 4175)
  • ...
  • 4175 / 4174 = 1.0002395783421 (the remainder is 1, so 4174 is not a divisor of 4175)
  • 4175 / 4175 = 1 (the remainder is 0, so 4175 is a divisor of 4175)

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 4175 (i.e. 64.6142399166). 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 )

  • 4175 / 1 = 4175 (the remainder is 0, so 1 and 4175 are divisors of 4175)
  • 4175 / 2 = 2087.5 (the remainder is 1, so 2 is not a divisor of 4175)
  • 4175 / 3 = 1391.6666666667 (the remainder is 2, so 3 is not a divisor of 4175)
  • ...
  • 4175 / 63 = 66.269841269841 (the remainder is 17, so 63 is not a divisor of 4175)
  • 4175 / 64 = 65.234375 (the remainder is 15, so 64 is not a divisor of 4175)