What are the divisors of 1752?

1, 2, 3, 4, 6, 8, 12, 24, 73, 146, 219, 292, 438, 584, 876, 1752

There is a total of 16 positive divisors.
The sum of these divisors is 4440.
The arithmetic mean is 277.5.

12 even divisors

2, 4, 6, 8, 12, 24, 146, 292, 438, 584, 876, 1752

4 odd divisors

1, 3, 73, 219

How to compute the divisors of 1752?

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 1752 by each of the numbers from 1 to 1752 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)

1752 / 1 = 1752 (the remainder is 0, so 1 is a divisor of 1752)
1752 / 2 = 876 (the remainder is 0, so 2 is a divisor of 1752)
1752 / 3 = 584 (the remainder is 0, so 3 is a divisor of 1752)
...
1752 / 1751 = 1.0005711022273 (the remainder is 1, so 1751 is not a divisor of 1752)
1752 / 1752 = 1 (the remainder is 0, so 1752 is a divisor of 1752)

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 1752 (i.e. 41.856899072913). 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 $\frac{N}{d} = D$ )

1752 / 1 = 1752 (the remainder is 0, so 1 and 1752 are divisors of 1752)
1752 / 2 = 876 (the remainder is 0, so 2 and 876 are divisors of 1752)
1752 / 3 = 584 (the remainder is 0, so 3 and 584 are divisors of 1752)
...
1752 / 40 = 43.8 (the remainder is 32, so 40 is not a divisor of 1752)
1752 / 41 = 42.731707317073 (the remainder is 30, so 41 is not a divisor of 1752)