What are the divisors of 4078?

1, 2, 2039, 4078

There is a total of 4 positive divisors.
The sum of these divisors is 6120.
The arithmetic mean is 1530.

2 even divisors

2, 4078

2 odd divisors

1, 2039

How to compute the divisors of 4078?

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 4078 by each of the numbers from 1 to 4078 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)

4078 / 1 = 4078 (the remainder is 0, so 1 is a divisor of 4078)
4078 / 2 = 2039 (the remainder is 0, so 2 is a divisor of 4078)
4078 / 3 = 1359.3333333333 (the remainder is 1, so 3 is not a divisor of 4078)
...
4078 / 4077 = 1.000245278391 (the remainder is 1, so 4077 is not a divisor of 4078)
4078 / 4078 = 1 (the remainder is 0, so 4078 is a divisor of 4078)

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 4078 (i.e. 63.859220164358). 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 $\frac{N}{d} = D$ )

4078 / 1 = 4078 (the remainder is 0, so 1 and 4078 are divisors of 4078)
4078 / 2 = 2039 (the remainder is 0, so 2 and 2039 are divisors of 4078)
4078 / 3 = 1359.3333333333 (the remainder is 1, so 3 is not a divisor of 4078)
...
4078 / 62 = 65.774193548387 (the remainder is 48, so 62 is not a divisor of 4078)
4078 / 63 = 64.730158730159 (the remainder is 46, so 63 is not a divisor of 4078)