What are the divisors of 1556?

1, 2, 4, 389, 778, 1556

There is a total of 6 positive divisors.
The sum of these divisors is 2730.
The arithmetic mean is 455.

4 even divisors

2, 4, 778, 1556

2 odd divisors

1, 389

How to compute the divisors of 1556?

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 1556 by each of the numbers from 1 to 1556 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)

1556 / 1 = 1556 (the remainder is 0, so 1 is a divisor of 1556)
1556 / 2 = 778 (the remainder is 0, so 2 is a divisor of 1556)
1556 / 3 = 518.66666666667 (the remainder is 2, so 3 is not a divisor of 1556)
...
1556 / 1555 = 1.0006430868167 (the remainder is 1, so 1555 is not a divisor of 1556)
1556 / 1556 = 1 (the remainder is 0, so 1556 is a divisor of 1556)

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 1556 (i.e. 39.446165846632). 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 $\frac{N}{d} = D$ )

1556 / 1 = 1556 (the remainder is 0, so 1 and 1556 are divisors of 1556)
1556 / 2 = 778 (the remainder is 0, so 2 and 778 are divisors of 1556)
1556 / 3 = 518.66666666667 (the remainder is 2, so 3 is not a divisor of 1556)
...
1556 / 38 = 40.947368421053 (the remainder is 36, so 38 is not a divisor of 1556)
1556 / 39 = 39.897435897436 (the remainder is 35, so 39 is not a divisor of 1556)