What are the divisors of 5550?

1, 2, 3, 5, 6, 10, 15, 25, 30, 37, 50, 74, 75, 111, 150, 185, 222, 370, 555, 925, 1110, 1850, 2775, 5550

12 even divisors

2, 6, 10, 30, 50, 74, 150, 222, 370, 1110, 1850, 5550

12 odd divisors

1, 3, 5, 15, 25, 37, 75, 111, 185, 555, 925, 2775

How to compute the divisors of 5550?

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 5550 by each of the numbers from 1 to 5550 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)

  • 5550 / 1 = 5550 (the remainder is 0, so 1 is a divisor of 5550)
  • 5550 / 2 = 2775 (the remainder is 0, so 2 is a divisor of 5550)
  • 5550 / 3 = 1850 (the remainder is 0, so 3 is a divisor of 5550)
  • ...
  • 5550 / 5549 = 1.0001802126509 (the remainder is 1, so 5549 is not a divisor of 5550)
  • 5550 / 5550 = 1 (the remainder is 0, so 5550 is a divisor of 5550)

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 5550 (i.e. 74.498322128757). 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 )

  • 5550 / 1 = 5550 (the remainder is 0, so 1 and 5550 are divisors of 5550)
  • 5550 / 2 = 2775 (the remainder is 0, so 2 and 2775 are divisors of 5550)
  • 5550 / 3 = 1850 (the remainder is 0, so 3 and 1850 are divisors of 5550)
  • ...
  • 5550 / 73 = 76.027397260274 (the remainder is 2, so 73 is not a divisor of 5550)
  • 5550 / 74 = 75 (the remainder is 0, so 74 and 75 are divisors of 5550)