What are the divisors of 3575?

1, 5, 11, 13, 25, 55, 65, 143, 275, 325, 715, 3575

There is a total of 12 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 434.

12 odd divisors

1, 5, 11, 13, 25, 55, 65, 143, 275, 325, 715, 3575

How to compute the divisors of 3575?

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 3575 by each of the numbers from 1 to 3575 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)

3575 / 1 = 3575 (the remainder is 0, so 1 is a divisor of 3575)
3575 / 2 = 1787.5 (the remainder is 1, so 2 is not a divisor of 3575)
3575 / 3 = 1191.6666666667 (the remainder is 2, so 3 is not a divisor of 3575)
...
3575 / 3574 = 1.000279798545 (the remainder is 1, so 3574 is not a divisor of 3575)
3575 / 3575 = 1 (the remainder is 0, so 3575 is a divisor of 3575)

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 3575 (i.e. 59.791303715507). 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 $\frac{N}{d} = D$ )

3575 / 1 = 3575 (the remainder is 0, so 1 and 3575 are divisors of 3575)
3575 / 2 = 1787.5 (the remainder is 1, so 2 is not a divisor of 3575)
3575 / 3 = 1191.6666666667 (the remainder is 2, so 3 is not a divisor of 3575)
...
3575 / 58 = 61.637931034483 (the remainder is 37, so 58 is not a divisor of 3575)
3575 / 59 = 60.593220338983 (the remainder is 35, so 59 is not a divisor of 3575)