What are the divisors of 3041?

1, 3041

There is a total of 2 positive divisors.
The sum of these divisors is 3042.
The arithmetic mean is 1521.

2 odd divisors

1, 3041

How to compute the divisors of 3041?

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 3041 by each of the numbers from 1 to 3041 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)

3041 / 1 = 3041 (the remainder is 0, so 1 is a divisor of 3041)
3041 / 2 = 1520.5 (the remainder is 1, so 2 is not a divisor of 3041)
3041 / 3 = 1013.6666666667 (the remainder is 2, so 3 is not a divisor of 3041)
...
3041 / 3040 = 1.0003289473684 (the remainder is 1, so 3040 is not a divisor of 3041)
3041 / 3041 = 1 (the remainder is 0, so 3041 is a divisor of 3041)

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 3041 (i.e. 55.145262715849). 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 $\frac{N}{d} = D$ )

3041 / 1 = 3041 (the remainder is 0, so 1 and 3041 are divisors of 3041)
3041 / 2 = 1520.5 (the remainder is 1, so 2 is not a divisor of 3041)
3041 / 3 = 1013.6666666667 (the remainder is 2, so 3 is not a divisor of 3041)
...
3041 / 54 = 56.314814814815 (the remainder is 17, so 54 is not a divisor of 3041)
3041 / 55 = 55.290909090909 (the remainder is 16, so 55 is not a divisor of 3041)