What are the divisors of 3276?

1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 26, 28, 36, 39, 42, 52, 63, 78, 84, 91, 117, 126, 156, 182, 234, 252, 273, 364, 468, 546, 819, 1092, 1638, 3276

There is a total of 36 positive divisors.
The sum of these divisors is 10192.
The arithmetic mean is 283.11111111111.

24 even divisors

2, 4, 6, 12, 14, 18, 26, 28, 36, 42, 52, 78, 84, 126, 156, 182, 234, 252, 364, 468, 546, 1092, 1638, 3276

12 odd divisors

1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819

How to compute the divisors of 3276?

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 3276 by each of the numbers from 1 to 3276 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)

3276 / 1 = 3276 (the remainder is 0, so 1 is a divisor of 3276)
3276 / 2 = 1638 (the remainder is 0, so 2 is a divisor of 3276)
3276 / 3 = 1092 (the remainder is 0, so 3 is a divisor of 3276)
...
3276 / 3275 = 1.0003053435115 (the remainder is 1, so 3275 is not a divisor of 3276)
3276 / 3276 = 1 (the remainder is 0, so 3276 is a divisor of 3276)

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 3276 (i.e. 57.236352085017). 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 $\frac{N}{d} = D$ )

3276 / 1 = 3276 (the remainder is 0, so 1 and 3276 are divisors of 3276)
3276 / 2 = 1638 (the remainder is 0, so 2 and 1638 are divisors of 3276)
3276 / 3 = 1092 (the remainder is 0, so 3 and 1092 are divisors of 3276)
...
3276 / 56 = 58.5 (the remainder is 28, so 56 is not a divisor of 3276)
3276 / 57 = 57.473684210526 (the remainder is 27, so 57 is not a divisor of 3276)