What are the divisors of 5554?

1, 2, 2777, 5554

There is a total of 4 positive divisors.
The sum of these divisors is 8334.
The arithmetic mean is 2083.5.

2 even divisors

2, 5554

2 odd divisors

1, 2777

How to compute the divisors of 5554?

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 5554 by each of the numbers from 1 to 5554 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5554 / 1 = 5554 (the remainder is 0, so 1 is a divisor of 5554)
5554 / 2 = 2777 (the remainder is 0, so 2 is a divisor of 5554)
5554 / 3 = 1851.3333333333 (the remainder is 1, so 3 is not a divisor of 5554)
...
5554 / 5553 = 1.0001800828381 (the remainder is 1, so 5553 is not a divisor of 5554)
5554 / 5554 = 1 (the remainder is 0, so 5554 is a divisor of 5554)

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 5554 (i.e. 74.525163535547). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5554 / 1 = 5554 (the remainder is 0, so 1 and 5554 are divisors of 5554)
5554 / 2 = 2777 (the remainder is 0, so 2 and 2777 are divisors of 5554)
5554 / 3 = 1851.3333333333 (the remainder is 1, so 3 is not a divisor of 5554)
...
5554 / 73 = 76.082191780822 (the remainder is 6, so 73 is not a divisor of 5554)
5554 / 74 = 75.054054054054 (the remainder is 4, so 74 is not a divisor of 5554)