What are the divisors of 4601?

1, 43, 107, 4601

There is a total of 4 positive divisors.
The sum of these divisors is 4752.
The arithmetic mean is 1188.

4 odd divisors

1, 43, 107, 4601

How to compute the divisors of 4601?

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 4601 by each of the numbers from 1 to 4601 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)

4601 / 1 = 4601 (the remainder is 0, so 1 is a divisor of 4601)
4601 / 2 = 2300.5 (the remainder is 1, so 2 is not a divisor of 4601)
4601 / 3 = 1533.6666666667 (the remainder is 2, so 3 is not a divisor of 4601)
...
4601 / 4600 = 1.0002173913043 (the remainder is 1, so 4600 is not a divisor of 4601)
4601 / 4601 = 1 (the remainder is 0, so 4601 is a divisor of 4601)

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 4601 (i.e. 67.830671528446). 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 $\frac{N}{d} = D$ )

4601 / 1 = 4601 (the remainder is 0, so 1 and 4601 are divisors of 4601)
4601 / 2 = 2300.5 (the remainder is 1, so 2 is not a divisor of 4601)
4601 / 3 = 1533.6666666667 (the remainder is 2, so 3 is not a divisor of 4601)
...
4601 / 66 = 69.712121212121 (the remainder is 47, so 66 is not a divisor of 4601)
4601 / 67 = 68.671641791045 (the remainder is 45, so 67 is not a divisor of 4601)