What are the divisors of 3752?

1, 2, 4, 7, 8, 14, 28, 56, 67, 134, 268, 469, 536, 938, 1876, 3752

There is a total of 16 positive divisors.
The sum of these divisors is 8160.
The arithmetic mean is 510.

12 even divisors

2, 4, 8, 14, 28, 56, 134, 268, 536, 938, 1876, 3752

4 odd divisors

1, 7, 67, 469

How to compute the divisors of 3752?

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 3752 by each of the numbers from 1 to 3752 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)

3752 / 1 = 3752 (the remainder is 0, so 1 is a divisor of 3752)
3752 / 2 = 1876 (the remainder is 0, so 2 is a divisor of 3752)
3752 / 3 = 1250.6666666667 (the remainder is 2, so 3 is not a divisor of 3752)
...
3752 / 3751 = 1.0002665955745 (the remainder is 1, so 3751 is not a divisor of 3752)
3752 / 3752 = 1 (the remainder is 0, so 3752 is a divisor of 3752)

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 3752 (i.e. 61.253571324454). 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 $\frac{N}{d} = D$ )

3752 / 1 = 3752 (the remainder is 0, so 1 and 3752 are divisors of 3752)
3752 / 2 = 1876 (the remainder is 0, so 2 and 1876 are divisors of 3752)
3752 / 3 = 1250.6666666667 (the remainder is 2, so 3 is not a divisor of 3752)
...
3752 / 60 = 62.533333333333 (the remainder is 32, so 60 is not a divisor of 3752)
3752 / 61 = 61.508196721311 (the remainder is 31, so 61 is not a divisor of 3752)