What are the divisors of 7105?

1, 5, 7, 29, 35, 49, 145, 203, 245, 1015, 1421, 7105

12 odd divisors

1, 5, 7, 29, 35, 49, 145, 203, 245, 1015, 1421, 7105

How to compute the divisors of 7105?

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 7105 by each of the numbers from 1 to 7105 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)

  • 7105 / 1 = 7105 (the remainder is 0, so 1 is a divisor of 7105)
  • 7105 / 2 = 3552.5 (the remainder is 1, so 2 is not a divisor of 7105)
  • 7105 / 3 = 2368.3333333333 (the remainder is 1, so 3 is not a divisor of 7105)
  • ...
  • 7105 / 7104 = 1.0001407657658 (the remainder is 1, so 7104 is not a divisor of 7105)
  • 7105 / 7105 = 1 (the remainder is 0, so 7105 is a divisor of 7105)

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 7105 (i.e. 84.291162051546). 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 )

  • 7105 / 1 = 7105 (the remainder is 0, so 1 and 7105 are divisors of 7105)
  • 7105 / 2 = 3552.5 (the remainder is 1, so 2 is not a divisor of 7105)
  • 7105 / 3 = 2368.3333333333 (the remainder is 1, so 3 is not a divisor of 7105)
  • ...
  • 7105 / 83 = 85.602409638554 (the remainder is 50, so 83 is not a divisor of 7105)
  • 7105 / 84 = 84.583333333333 (the remainder is 49, so 84 is not a divisor of 7105)