What are the divisors of 1554?

1, 2, 3, 6, 7, 14, 21, 37, 42, 74, 111, 222, 259, 518, 777, 1554

There is a total of 16 positive divisors.
The sum of these divisors is 3648.
The arithmetic mean is 228.

8 even divisors

2, 6, 14, 42, 74, 222, 518, 1554

8 odd divisors

1, 3, 7, 21, 37, 111, 259, 777

How to compute the divisors of 1554?

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 1554 by each of the numbers from 1 to 1554 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)

1554 / 1 = 1554 (the remainder is 0, so 1 is a divisor of 1554)
1554 / 2 = 777 (the remainder is 0, so 2 is a divisor of 1554)
1554 / 3 = 518 (the remainder is 0, so 3 is a divisor of 1554)
...
1554 / 1553 = 1.0006439150032 (the remainder is 1, so 1553 is not a divisor of 1554)
1554 / 1554 = 1 (the remainder is 0, so 1554 is a divisor of 1554)

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 1554 (i.e. 39.420806688854). 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 $\frac{N}{d} = D$ )

1554 / 1 = 1554 (the remainder is 0, so 1 and 1554 are divisors of 1554)
1554 / 2 = 777 (the remainder is 0, so 2 and 777 are divisors of 1554)
1554 / 3 = 518 (the remainder is 0, so 3 and 518 are divisors of 1554)
...
1554 / 38 = 40.894736842105 (the remainder is 34, so 38 is not a divisor of 1554)
1554 / 39 = 39.846153846154 (the remainder is 33, so 39 is not a divisor of 1554)