What are the divisors of 2779?

1, 7, 397, 2779

There is a total of 4 positive divisors.
The sum of these divisors is 3184.
The arithmetic mean is 796.

4 odd divisors

1, 7, 397, 2779

How to compute the divisors of 2779?

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 2779 by each of the numbers from 1 to 2779 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)

2779 / 1 = 2779 (the remainder is 0, so 1 is a divisor of 2779)
2779 / 2 = 1389.5 (the remainder is 1, so 2 is not a divisor of 2779)
2779 / 3 = 926.33333333333 (the remainder is 1, so 3 is not a divisor of 2779)
...
2779 / 2778 = 1.0003599712023 (the remainder is 1, so 2778 is not a divisor of 2779)
2779 / 2779 = 1 (the remainder is 0, so 2779 is a divisor of 2779)

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 2779 (i.e. 52.716221412389). 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 $\frac{N}{d} = D$ )

2779 / 1 = 2779 (the remainder is 0, so 1 and 2779 are divisors of 2779)
2779 / 2 = 1389.5 (the remainder is 1, so 2 is not a divisor of 2779)
2779 / 3 = 926.33333333333 (the remainder is 1, so 3 is not a divisor of 2779)
...
2779 / 51 = 54.490196078431 (the remainder is 25, so 51 is not a divisor of 2779)
2779 / 52 = 53.442307692308 (the remainder is 23, so 52 is not a divisor of 2779)