What are the divisors of 4675?

1, 5, 11, 17, 25, 55, 85, 187, 275, 425, 935, 4675

There is a total of 12 positive divisors.
The sum of these divisors is 6696.
The arithmetic mean is 558.

12 odd divisors

1, 5, 11, 17, 25, 55, 85, 187, 275, 425, 935, 4675

How to compute the divisors of 4675?

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 4675 by each of the numbers from 1 to 4675 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)

4675 / 1 = 4675 (the remainder is 0, so 1 is a divisor of 4675)
4675 / 2 = 2337.5 (the remainder is 1, so 2 is not a divisor of 4675)
4675 / 3 = 1558.3333333333 (the remainder is 1, so 3 is not a divisor of 4675)
...
4675 / 4674 = 1.0002139495079 (the remainder is 1, so 4674 is not a divisor of 4675)
4675 / 4675 = 1 (the remainder is 0, so 4675 is a divisor of 4675)

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 4675 (i.e. 68.373971655887). 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 $\frac{N}{d} = D$ )

4675 / 1 = 4675 (the remainder is 0, so 1 and 4675 are divisors of 4675)
4675 / 2 = 2337.5 (the remainder is 1, so 2 is not a divisor of 4675)
4675 / 3 = 1558.3333333333 (the remainder is 1, so 3 is not a divisor of 4675)
...
4675 / 67 = 69.776119402985 (the remainder is 52, so 67 is not a divisor of 4675)
4675 / 68 = 68.75 (the remainder is 51, so 68 is not a divisor of 4675)