What are the divisors of 3776?

1, 2, 4, 8, 16, 32, 59, 64, 118, 236, 472, 944, 1888, 3776

There is a total of 14 positive divisors.
The sum of these divisors is 7620.
The arithmetic mean is 544.28571428571.

12 even divisors

2, 4, 8, 16, 32, 64, 118, 236, 472, 944, 1888, 3776

2 odd divisors

1, 59

How to compute the divisors of 3776?

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 3776 by each of the numbers from 1 to 3776 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)

3776 / 1 = 3776 (the remainder is 0, so 1 is a divisor of 3776)
3776 / 2 = 1888 (the remainder is 0, so 2 is a divisor of 3776)
3776 / 3 = 1258.6666666667 (the remainder is 2, so 3 is not a divisor of 3776)
...
3776 / 3775 = 1.0002649006623 (the remainder is 1, so 3775 is not a divisor of 3776)
3776 / 3776 = 1 (the remainder is 0, so 3776 is a divisor of 3776)

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 3776 (i.e. 61.449165982949). 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 $\frac{N}{d} = D$ )

3776 / 1 = 3776 (the remainder is 0, so 1 and 3776 are divisors of 3776)
3776 / 2 = 1888 (the remainder is 0, so 2 and 1888 are divisors of 3776)
3776 / 3 = 1258.6666666667 (the remainder is 2, so 3 is not a divisor of 3776)
...
3776 / 60 = 62.933333333333 (the remainder is 56, so 60 is not a divisor of 3776)
3776 / 61 = 61.901639344262 (the remainder is 55, so 61 is not a divisor of 3776)