What are the divisors of 3675?

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675

There is a total of 18 positive divisors.
The sum of these divisors is 7068.
The arithmetic mean is 392.66666666667.

18 odd divisors

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 525, 735, 1225, 3675

How to compute the divisors of 3675?

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 3675 by each of the numbers from 1 to 3675 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)

3675 / 1 = 3675 (the remainder is 0, so 1 is a divisor of 3675)
3675 / 2 = 1837.5 (the remainder is 1, so 2 is not a divisor of 3675)
3675 / 3 = 1225 (the remainder is 0, so 3 is a divisor of 3675)
...
3675 / 3674 = 1.0002721829069 (the remainder is 1, so 3674 is not a divisor of 3675)
3675 / 3675 = 1 (the remainder is 0, so 3675 is a divisor of 3675)

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 3675 (i.e. 60.621778264911). 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 $\frac{N}{d} = D$ )

3675 / 1 = 3675 (the remainder is 0, so 1 and 3675 are divisors of 3675)
3675 / 2 = 1837.5 (the remainder is 1, so 2 is not a divisor of 3675)
3675 / 3 = 1225 (the remainder is 0, so 3 and 1225 are divisors of 3675)
...
3675 / 59 = 62.28813559322 (the remainder is 17, so 59 is not a divisor of 3675)
3675 / 60 = 61.25 (the remainder is 15, so 60 is not a divisor of 3675)