What are the divisors of 3656?

1, 2, 4, 8, 457, 914, 1828, 3656

6 even divisors

2, 4, 8, 914, 1828, 3656

2 odd divisors

1, 457

How to compute the divisors of 3656?

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 3656 by each of the numbers from 1 to 3656 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)

  • 3656 / 1 = 3656 (the remainder is 0, so 1 is a divisor of 3656)
  • 3656 / 2 = 1828 (the remainder is 0, so 2 is a divisor of 3656)
  • 3656 / 3 = 1218.6666666667 (the remainder is 2, so 3 is not a divisor of 3656)
  • ...
  • 3656 / 3655 = 1.0002735978112 (the remainder is 1, so 3655 is not a divisor of 3656)
  • 3656 / 3656 = 1 (the remainder is 0, so 3656 is a divisor of 3656)

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 3656 (i.e. 60.464865831324). 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 )

  • 3656 / 1 = 3656 (the remainder is 0, so 1 and 3656 are divisors of 3656)
  • 3656 / 2 = 1828 (the remainder is 0, so 2 and 1828 are divisors of 3656)
  • 3656 / 3 = 1218.6666666667 (the remainder is 2, so 3 is not a divisor of 3656)
  • ...
  • 3656 / 59 = 61.966101694915 (the remainder is 57, so 59 is not a divisor of 3656)
  • 3656 / 60 = 60.933333333333 (the remainder is 56, so 60 is not a divisor of 3656)