What are the divisors of 4077?

1, 3, 9, 27, 151, 453, 1359, 4077

There is a total of 8 positive divisors.
The sum of these divisors is 6080.
The arithmetic mean is 760.

8 odd divisors

1, 3, 9, 27, 151, 453, 1359, 4077

How to compute the divisors of 4077?

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 4077 by each of the numbers from 1 to 4077 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)

4077 / 1 = 4077 (the remainder is 0, so 1 is a divisor of 4077)
4077 / 2 = 2038.5 (the remainder is 1, so 2 is not a divisor of 4077)
4077 / 3 = 1359 (the remainder is 0, so 3 is a divisor of 4077)
...
4077 / 4076 = 1.0002453385672 (the remainder is 1, so 4076 is not a divisor of 4077)
4077 / 4077 = 1 (the remainder is 0, so 4077 is a divisor of 4077)

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 4077 (i.e. 63.851389961378). 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 $\frac{N}{d} = D$ )

4077 / 1 = 4077 (the remainder is 0, so 1 and 4077 are divisors of 4077)
4077 / 2 = 2038.5 (the remainder is 1, so 2 is not a divisor of 4077)
4077 / 3 = 1359 (the remainder is 0, so 3 and 1359 are divisors of 4077)
...
4077 / 62 = 65.758064516129 (the remainder is 47, so 62 is not a divisor of 4077)
4077 / 63 = 64.714285714286 (the remainder is 45, so 63 is not a divisor of 4077)