What are the divisors of 2941?

1, 17, 173, 2941

There is a total of 4 positive divisors.
The sum of these divisors is 3132.
The arithmetic mean is 783.

4 odd divisors

1, 17, 173, 2941

How to compute the divisors of 2941?

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 2941 by each of the numbers from 1 to 2941 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)

2941 / 1 = 2941 (the remainder is 0, so 1 is a divisor of 2941)
2941 / 2 = 1470.5 (the remainder is 1, so 2 is not a divisor of 2941)
2941 / 3 = 980.33333333333 (the remainder is 1, so 3 is not a divisor of 2941)
...
2941 / 2940 = 1.0003401360544 (the remainder is 1, so 2940 is not a divisor of 2941)
2941 / 2941 = 1 (the remainder is 0, so 2941 is a divisor of 2941)

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 2941 (i.e. 54.230987451825). 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 $\frac{N}{d} = D$ )

2941 / 1 = 2941 (the remainder is 0, so 1 and 2941 are divisors of 2941)
2941 / 2 = 1470.5 (the remainder is 1, so 2 is not a divisor of 2941)
2941 / 3 = 980.33333333333 (the remainder is 1, so 3 is not a divisor of 2941)
...
2941 / 53 = 55.490566037736 (the remainder is 26, so 53 is not a divisor of 2941)
2941 / 54 = 54.462962962963 (the remainder is 25, so 54 is not a divisor of 2941)