What are the divisors of 2981?

1, 11, 271, 2981

There is a total of 4 positive divisors.
The sum of these divisors is 3264.
The arithmetic mean is 816.

4 odd divisors

1, 11, 271, 2981

How to compute the divisors of 2981?

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 2981 by each of the numbers from 1 to 2981 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)

2981 / 1 = 2981 (the remainder is 0, so 1 is a divisor of 2981)
2981 / 2 = 1490.5 (the remainder is 1, so 2 is not a divisor of 2981)
2981 / 3 = 993.66666666667 (the remainder is 2, so 3 is not a divisor of 2981)
...
2981 / 2980 = 1.0003355704698 (the remainder is 1, so 2980 is not a divisor of 2981)
2981 / 2981 = 1 (the remainder is 0, so 2981 is a divisor of 2981)

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 2981 (i.e. 54.598534778875). 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 $\frac{N}{d} = D$ )

2981 / 1 = 2981 (the remainder is 0, so 1 and 2981 are divisors of 2981)
2981 / 2 = 1490.5 (the remainder is 1, so 2 is not a divisor of 2981)
2981 / 3 = 993.66666666667 (the remainder is 2, so 3 is not a divisor of 2981)
...
2981 / 53 = 56.245283018868 (the remainder is 13, so 53 is not a divisor of 2981)
2981 / 54 = 55.203703703704 (the remainder is 11, so 54 is not a divisor of 2981)