What are the divisors of 5901?

1, 3, 7, 21, 281, 843, 1967, 5901

There is a total of 8 positive divisors.
The sum of these divisors is 9024.
The arithmetic mean is 1128.

8 odd divisors

1, 3, 7, 21, 281, 843, 1967, 5901

How to compute the divisors of 5901?

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 5901 by each of the numbers from 1 to 5901 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)

5901 / 1 = 5901 (the remainder is 0, so 1 is a divisor of 5901)
5901 / 2 = 2950.5 (the remainder is 1, so 2 is not a divisor of 5901)
5901 / 3 = 1967 (the remainder is 0, so 3 is a divisor of 5901)
...
5901 / 5900 = 1.0001694915254 (the remainder is 1, so 5900 is not a divisor of 5901)
5901 / 5901 = 1 (the remainder is 0, so 5901 is a divisor of 5901)

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 5901 (i.e. 76.817966648435). 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 $\frac{N}{d} = D$ )

5901 / 1 = 5901 (the remainder is 0, so 1 and 5901 are divisors of 5901)
5901 / 2 = 2950.5 (the remainder is 1, so 2 is not a divisor of 5901)
5901 / 3 = 1967 (the remainder is 0, so 3 and 1967 are divisors of 5901)
...
5901 / 75 = 78.68 (the remainder is 51, so 75 is not a divisor of 5901)
5901 / 76 = 77.644736842105 (the remainder is 49, so 76 is not a divisor of 5901)