What are the divisors of 4655?

1, 5, 7, 19, 35, 49, 95, 133, 245, 665, 931, 4655

There is a total of 12 positive divisors.
The sum of these divisors is 6840.
The arithmetic mean is 570.

12 odd divisors

1, 5, 7, 19, 35, 49, 95, 133, 245, 665, 931, 4655

How to compute the divisors of 4655?

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 4655 by each of the numbers from 1 to 4655 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)

4655 / 1 = 4655 (the remainder is 0, so 1 is a divisor of 4655)
4655 / 2 = 2327.5 (the remainder is 1, so 2 is not a divisor of 4655)
4655 / 3 = 1551.6666666667 (the remainder is 2, so 3 is not a divisor of 4655)
...
4655 / 4654 = 1.00021486893 (the remainder is 1, so 4654 is not a divisor of 4655)
4655 / 4655 = 1 (the remainder is 0, so 4655 is a divisor of 4655)

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 4655 (i.e. 68.227560413663). 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 $\frac{N}{d} = D$ )

4655 / 1 = 4655 (the remainder is 0, so 1 and 4655 are divisors of 4655)
4655 / 2 = 2327.5 (the remainder is 1, so 2 is not a divisor of 4655)
4655 / 3 = 1551.6666666667 (the remainder is 2, so 3 is not a divisor of 4655)
...
4655 / 67 = 69.477611940299 (the remainder is 32, so 67 is not a divisor of 4655)
4655 / 68 = 68.455882352941 (the remainder is 31, so 68 is not a divisor of 4655)