What are the divisors of 2077?

1, 31, 67, 2077

There is a total of 4 positive divisors.
The sum of these divisors is 2176.
The arithmetic mean is 544.

4 odd divisors

1, 31, 67, 2077

How to compute the divisors of 2077?

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 2077 by each of the numbers from 1 to 2077 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)

2077 / 1 = 2077 (the remainder is 0, so 1 is a divisor of 2077)
2077 / 2 = 1038.5 (the remainder is 1, so 2 is not a divisor of 2077)
2077 / 3 = 692.33333333333 (the remainder is 1, so 3 is not a divisor of 2077)
...
2077 / 2076 = 1.0004816955684 (the remainder is 1, so 2076 is not a divisor of 2077)
2077 / 2077 = 1 (the remainder is 0, so 2077 is a divisor of 2077)

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 2077 (i.e. 45.574115460423). 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 $\frac{N}{d} = D$ )

2077 / 1 = 2077 (the remainder is 0, so 1 and 2077 are divisors of 2077)
2077 / 2 = 1038.5 (the remainder is 1, so 2 is not a divisor of 2077)
2077 / 3 = 692.33333333333 (the remainder is 1, so 3 is not a divisor of 2077)
...
2077 / 44 = 47.204545454545 (the remainder is 9, so 44 is not a divisor of 2077)
2077 / 45 = 46.155555555556 (the remainder is 7, so 45 is not a divisor of 2077)