What are the divisors of 1544?

1, 2, 4, 8, 193, 386, 772, 1544

There is a total of 8 positive divisors.
The sum of these divisors is 2910.
The arithmetic mean is 363.75.

6 even divisors

2, 4, 8, 386, 772, 1544

2 odd divisors

1, 193

How to compute the divisors of 1544?

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 1544 by each of the numbers from 1 to 1544 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)

1544 / 1 = 1544 (the remainder is 0, so 1 is a divisor of 1544)
1544 / 2 = 772 (the remainder is 0, so 2 is a divisor of 1544)
1544 / 3 = 514.66666666667 (the remainder is 2, so 3 is not a divisor of 1544)
...
1544 / 1543 = 1.00064808814 (the remainder is 1, so 1543 is not a divisor of 1544)
1544 / 1544 = 1 (the remainder is 0, so 1544 is a divisor of 1544)

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 1544 (i.e. 39.293765408777). 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 $\frac{N}{d} = D$ )

1544 / 1 = 1544 (the remainder is 0, so 1 and 1544 are divisors of 1544)
1544 / 2 = 772 (the remainder is 0, so 2 and 772 are divisors of 1544)
1544 / 3 = 514.66666666667 (the remainder is 2, so 3 is not a divisor of 1544)
...
1544 / 38 = 40.631578947368 (the remainder is 24, so 38 is not a divisor of 1544)
1544 / 39 = 39.589743589744 (the remainder is 23, so 39 is not a divisor of 1544)