What are the divisors of 3672?

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 27, 34, 36, 51, 54, 68, 72, 102, 108, 136, 153, 204, 216, 306, 408, 459, 612, 918, 1224, 1836, 3672

There is a total of 32 positive divisors.
The sum of these divisors is 10800.
The arithmetic mean is 337.5.

24 even divisors

2, 4, 6, 8, 12, 18, 24, 34, 36, 54, 68, 72, 102, 108, 136, 204, 216, 306, 408, 612, 918, 1224, 1836, 3672

8 odd divisors

1, 3, 9, 17, 27, 51, 153, 459

How to compute the divisors of 3672?

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 3672 by each of the numbers from 1 to 3672 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)

3672 / 1 = 3672 (the remainder is 0, so 1 is a divisor of 3672)
3672 / 2 = 1836 (the remainder is 0, so 2 is a divisor of 3672)
3672 / 3 = 1224 (the remainder is 0, so 3 is a divisor of 3672)
...
3672 / 3671 = 1.0002724053391 (the remainder is 1, so 3671 is not a divisor of 3672)
3672 / 3672 = 1 (the remainder is 0, so 3672 is a divisor of 3672)

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 3672 (i.e. 60.597029630172). 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 $\frac{N}{d} = D$ )

3672 / 1 = 3672 (the remainder is 0, so 1 and 3672 are divisors of 3672)
3672 / 2 = 1836 (the remainder is 0, so 2 and 1836 are divisors of 3672)
3672 / 3 = 1224 (the remainder is 0, so 3 and 1224 are divisors of 3672)
...
3672 / 59 = 62.237288135593 (the remainder is 14, so 59 is not a divisor of 3672)
3672 / 60 = 61.2 (the remainder is 12, so 60 is not a divisor of 3672)