What are the divisors of 1504?

1, 2, 4, 8, 16, 32, 47, 94, 188, 376, 752, 1504

There is a total of 12 positive divisors.
The sum of these divisors is 3024.
The arithmetic mean is 252.

10 even divisors

2, 4, 8, 16, 32, 94, 188, 376, 752, 1504

2 odd divisors

1, 47

How to compute the divisors of 1504?

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 1504 by each of the numbers from 1 to 1504 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)

1504 / 1 = 1504 (the remainder is 0, so 1 is a divisor of 1504)
1504 / 2 = 752 (the remainder is 0, so 2 is a divisor of 1504)
1504 / 3 = 501.33333333333 (the remainder is 1, so 3 is not a divisor of 1504)
...
1504 / 1503 = 1.0006653359947 (the remainder is 1, so 1503 is not a divisor of 1504)
1504 / 1504 = 1 (the remainder is 0, so 1504 is a divisor of 1504)

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 1504 (i.e. 38.781438859331). 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 $\frac{N}{d} = D$ )

1504 / 1 = 1504 (the remainder is 0, so 1 and 1504 are divisors of 1504)
1504 / 2 = 752 (the remainder is 0, so 2 and 752 are divisors of 1504)
1504 / 3 = 501.33333333333 (the remainder is 1, so 3 is not a divisor of 1504)
...
1504 / 37 = 40.648648648649 (the remainder is 24, so 37 is not a divisor of 1504)
1504 / 38 = 39.578947368421 (the remainder is 22, so 38 is not a divisor of 1504)