What are the divisors of 2801?

1, 2801

There is a total of 2 positive divisors.
The sum of these divisors is 2802.
The arithmetic mean is 1401.

2 odd divisors

1, 2801

How to compute the divisors of 2801?

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 2801 by each of the numbers from 1 to 2801 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)

2801 / 1 = 2801 (the remainder is 0, so 1 is a divisor of 2801)
2801 / 2 = 1400.5 (the remainder is 1, so 2 is not a divisor of 2801)
2801 / 3 = 933.66666666667 (the remainder is 2, so 3 is not a divisor of 2801)
...
2801 / 2800 = 1.0003571428571 (the remainder is 1, so 2800 is not a divisor of 2801)
2801 / 2801 = 1 (the remainder is 0, so 2801 is a divisor of 2801)

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 2801 (i.e. 52.924474489597). 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 $\frac{N}{d} = D$ )

2801 / 1 = 2801 (the remainder is 0, so 1 and 2801 are divisors of 2801)
2801 / 2 = 1400.5 (the remainder is 1, so 2 is not a divisor of 2801)
2801 / 3 = 933.66666666667 (the remainder is 2, so 3 is not a divisor of 2801)
...
2801 / 51 = 54.921568627451 (the remainder is 47, so 51 is not a divisor of 2801)
2801 / 52 = 53.865384615385 (the remainder is 45, so 52 is not a divisor of 2801)