What are the divisors of 2078?

1, 2, 1039, 2078

There is a total of 4 positive divisors.
The sum of these divisors is 3120.
The arithmetic mean is 780.

2 even divisors

2, 2078

2 odd divisors

1, 1039

How to compute the divisors of 2078?

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 2078 by each of the numbers from 1 to 2078 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)

2078 / 1 = 2078 (the remainder is 0, so 1 is a divisor of 2078)
2078 / 2 = 1039 (the remainder is 0, so 2 is a divisor of 2078)
2078 / 3 = 692.66666666667 (the remainder is 2, so 3 is not a divisor of 2078)
...
2078 / 2077 = 1.0004814636495 (the remainder is 1, so 2077 is not a divisor of 2078)
2078 / 2078 = 1 (the remainder is 0, so 2078 is a divisor of 2078)

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 2078 (i.e. 45.585085280166). 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 $\frac{N}{d} = D$ )

2078 / 1 = 2078 (the remainder is 0, so 1 and 2078 are divisors of 2078)
2078 / 2 = 1039 (the remainder is 0, so 2 and 1039 are divisors of 2078)
2078 / 3 = 692.66666666667 (the remainder is 2, so 3 is not a divisor of 2078)
...
2078 / 44 = 47.227272727273 (the remainder is 10, so 44 is not a divisor of 2078)
2078 / 45 = 46.177777777778 (the remainder is 8, so 45 is not a divisor of 2078)