What are the divisors of 2677?

1, 2677

There is a total of 2 positive divisors.
The sum of these divisors is 2678.
The arithmetic mean is 1339.

2 odd divisors

1, 2677

How to compute the divisors of 2677?

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 2677 by each of the numbers from 1 to 2677 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)

2677 / 1 = 2677 (the remainder is 0, so 1 is a divisor of 2677)
2677 / 2 = 1338.5 (the remainder is 1, so 2 is not a divisor of 2677)
2677 / 3 = 892.33333333333 (the remainder is 1, so 3 is not a divisor of 2677)
...
2677 / 2676 = 1.0003736920777 (the remainder is 1, so 2676 is not a divisor of 2677)
2677 / 2677 = 1 (the remainder is 0, so 2677 is a divisor of 2677)

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 2677 (i.e. 51.739733281106). 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 $\frac{N}{d} = D$ )

2677 / 1 = 2677 (the remainder is 0, so 1 and 2677 are divisors of 2677)
2677 / 2 = 1338.5 (the remainder is 1, so 2 is not a divisor of 2677)
2677 / 3 = 892.33333333333 (the remainder is 1, so 3 is not a divisor of 2677)
...
2677 / 50 = 53.54 (the remainder is 27, so 50 is not a divisor of 2677)
2677 / 51 = 52.490196078431 (the remainder is 25, so 51 is not a divisor of 2677)