What are the divisors of 2780?

1, 2, 4, 5, 10, 20, 139, 278, 556, 695, 1390, 2780

There is a total of 12 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 490.

8 even divisors

2, 4, 10, 20, 278, 556, 1390, 2780

4 odd divisors

1, 5, 139, 695

How to compute the divisors of 2780?

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 2780 by each of the numbers from 1 to 2780 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)

2780 / 1 = 2780 (the remainder is 0, so 1 is a divisor of 2780)
2780 / 2 = 1390 (the remainder is 0, so 2 is a divisor of 2780)
2780 / 3 = 926.66666666667 (the remainder is 2, so 3 is not a divisor of 2780)
...
2780 / 2779 = 1.0003598416697 (the remainder is 1, so 2779 is not a divisor of 2780)
2780 / 2780 = 1 (the remainder is 0, so 2780 is a divisor of 2780)

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 2780 (i.e. 52.725705305856). 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 $\frac{N}{d} = D$ )

2780 / 1 = 2780 (the remainder is 0, so 1 and 2780 are divisors of 2780)
2780 / 2 = 1390 (the remainder is 0, so 2 and 1390 are divisors of 2780)
2780 / 3 = 926.66666666667 (the remainder is 2, so 3 is not a divisor of 2780)
...
2780 / 51 = 54.509803921569 (the remainder is 26, so 51 is not a divisor of 2780)
2780 / 52 = 53.461538461538 (the remainder is 24, so 52 is not a divisor of 2780)