What are the divisors of 5494?

1, 2, 41, 67, 82, 134, 2747, 5494

4 even divisors

2, 82, 134, 5494

4 odd divisors

1, 41, 67, 2747

How to compute the divisors of 5494?

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 5494 by each of the numbers from 1 to 5494 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)

  • 5494 / 1 = 5494 (the remainder is 0, so 1 is a divisor of 5494)
  • 5494 / 2 = 2747 (the remainder is 0, so 2 is a divisor of 5494)
  • 5494 / 3 = 1831.3333333333 (the remainder is 1, so 3 is not a divisor of 5494)
  • ...
  • 5494 / 5493 = 1.0001820498817 (the remainder is 1, so 5493 is not a divisor of 5494)
  • 5494 / 5494 = 1 (the remainder is 0, so 5494 is a divisor of 5494)

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 5494 (i.e. 74.121521840826). 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 )

  • 5494 / 1 = 5494 (the remainder is 0, so 1 and 5494 are divisors of 5494)
  • 5494 / 2 = 2747 (the remainder is 0, so 2 and 2747 are divisors of 5494)
  • 5494 / 3 = 1831.3333333333 (the remainder is 1, so 3 is not a divisor of 5494)
  • ...
  • 5494 / 73 = 75.260273972603 (the remainder is 19, so 73 is not a divisor of 5494)
  • 5494 / 74 = 74.243243243243 (the remainder is 18, so 74 is not a divisor of 5494)