What are the divisors of 2877?

1, 3, 7, 21, 137, 411, 959, 2877

There is a total of 8 positive divisors.
The sum of these divisors is 4416.
The arithmetic mean is 552.

8 odd divisors

1, 3, 7, 21, 137, 411, 959, 2877

How to compute the divisors of 2877?

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 2877 by each of the numbers from 1 to 2877 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)

2877 / 1 = 2877 (the remainder is 0, so 1 is a divisor of 2877)
2877 / 2 = 1438.5 (the remainder is 1, so 2 is not a divisor of 2877)
2877 / 3 = 959 (the remainder is 0, so 3 is a divisor of 2877)
...
2877 / 2876 = 1.000347705146 (the remainder is 1, so 2876 is not a divisor of 2877)
2877 / 2877 = 1 (the remainder is 0, so 2877 is a divisor of 2877)

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 2877 (i.e. 53.637673327616). 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 $\frac{N}{d} = D$ )

2877 / 1 = 2877 (the remainder is 0, so 1 and 2877 are divisors of 2877)
2877 / 2 = 1438.5 (the remainder is 1, so 2 is not a divisor of 2877)
2877 / 3 = 959 (the remainder is 0, so 3 and 959 are divisors of 2877)
...
2877 / 52 = 55.326923076923 (the remainder is 17, so 52 is not a divisor of 2877)
2877 / 53 = 54.283018867925 (the remainder is 15, so 53 is not a divisor of 2877)