What are the divisors of 3712?

1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 464, 928, 1856, 3712

There is a total of 16 positive divisors.
The sum of these divisors is 7650.
The arithmetic mean is 478.125.

14 even divisors

2, 4, 8, 16, 32, 58, 64, 116, 128, 232, 464, 928, 1856, 3712

2 odd divisors

1, 29

How to compute the divisors of 3712?

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 3712 by each of the numbers from 1 to 3712 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)

3712 / 1 = 3712 (the remainder is 0, so 1 is a divisor of 3712)
3712 / 2 = 1856 (the remainder is 0, so 2 is a divisor of 3712)
3712 / 3 = 1237.3333333333 (the remainder is 1, so 3 is not a divisor of 3712)
...
3712 / 3711 = 1.0002694691458 (the remainder is 1, so 3711 is not a divisor of 3712)
3712 / 3712 = 1 (the remainder is 0, so 3712 is a divisor of 3712)

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 3712 (i.e. 60.926184846911). 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 $\frac{N}{d} = D$ )

3712 / 1 = 3712 (the remainder is 0, so 1 and 3712 are divisors of 3712)
3712 / 2 = 1856 (the remainder is 0, so 2 and 1856 are divisors of 3712)
3712 / 3 = 1237.3333333333 (the remainder is 1, so 3 is not a divisor of 3712)
...
3712 / 59 = 62.915254237288 (the remainder is 54, so 59 is not a divisor of 3712)
3712 / 60 = 61.866666666667 (the remainder is 52, so 60 is not a divisor of 3712)