What are the divisors of 2057?

1, 11, 17, 121, 187, 2057

There is a total of 6 positive divisors.
The sum of these divisors is 2394.
The arithmetic mean is 399.

6 odd divisors

1, 11, 17, 121, 187, 2057

How to compute the divisors of 2057?

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 2057 by each of the numbers from 1 to 2057 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)

2057 / 1 = 2057 (the remainder is 0, so 1 is a divisor of 2057)
2057 / 2 = 1028.5 (the remainder is 1, so 2 is not a divisor of 2057)
2057 / 3 = 685.66666666667 (the remainder is 2, so 3 is not a divisor of 2057)
...
2057 / 2056 = 1.000486381323 (the remainder is 1, so 2056 is not a divisor of 2057)
2057 / 2057 = 1 (the remainder is 0, so 2057 is a divisor of 2057)

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 2057 (i.e. 45.354161881794). 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 $\frac{N}{d} = D$ )

2057 / 1 = 2057 (the remainder is 0, so 1 and 2057 are divisors of 2057)
2057 / 2 = 1028.5 (the remainder is 1, so 2 is not a divisor of 2057)
2057 / 3 = 685.66666666667 (the remainder is 2, so 3 is not a divisor of 2057)
...
2057 / 44 = 46.75 (the remainder is 33, so 44 is not a divisor of 2057)
2057 / 45 = 45.711111111111 (the remainder is 32, so 45 is not a divisor of 2057)