What are the divisors of 5570?

1, 2, 5, 10, 557, 1114, 2785, 5570

4 even divisors

2, 10, 1114, 5570

4 odd divisors

1, 5, 557, 2785

How to compute the divisors of 5570?

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 5570 by each of the numbers from 1 to 5570 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)

  • 5570 / 1 = 5570 (the remainder is 0, so 1 is a divisor of 5570)
  • 5570 / 2 = 2785 (the remainder is 0, so 2 is a divisor of 5570)
  • 5570 / 3 = 1856.6666666667 (the remainder is 2, so 3 is not a divisor of 5570)
  • ...
  • 5570 / 5569 = 1.0001795654516 (the remainder is 1, so 5569 is not a divisor of 5570)
  • 5570 / 5570 = 1 (the remainder is 0, so 5570 is a divisor of 5570)

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 5570 (i.e. 74.632432628181). 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 )

  • 5570 / 1 = 5570 (the remainder is 0, so 1 and 5570 are divisors of 5570)
  • 5570 / 2 = 2785 (the remainder is 0, so 2 and 2785 are divisors of 5570)
  • 5570 / 3 = 1856.6666666667 (the remainder is 2, so 3 is not a divisor of 5570)
  • ...
  • 5570 / 73 = 76.301369863014 (the remainder is 22, so 73 is not a divisor of 5570)
  • 5570 / 74 = 75.27027027027 (the remainder is 20, so 74 is not a divisor of 5570)