What are the divisors of 7077?

1, 3, 7, 21, 337, 1011, 2359, 7077

There is a total of 8 positive divisors.
The sum of these divisors is 10816.
The arithmetic mean is 1352.

8 odd divisors

1, 3, 7, 21, 337, 1011, 2359, 7077

How to compute the divisors of 7077?

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 7077 by each of the numbers from 1 to 7077 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)

7077 / 1 = 7077 (the remainder is 0, so 1 is a divisor of 7077)
7077 / 2 = 3538.5 (the remainder is 1, so 2 is not a divisor of 7077)
7077 / 3 = 2359 (the remainder is 0, so 3 is a divisor of 7077)
...
7077 / 7076 = 1.0001413227812 (the remainder is 1, so 7076 is not a divisor of 7077)
7077 / 7077 = 1 (the remainder is 0, so 7077 is a divisor of 7077)

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 7077 (i.e. 84.124907132192). 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 $\frac{N}{d} = D$ )

7077 / 1 = 7077 (the remainder is 0, so 1 and 7077 are divisors of 7077)
7077 / 2 = 3538.5 (the remainder is 1, so 2 is not a divisor of 7077)
7077 / 3 = 2359 (the remainder is 0, so 3 and 2359 are divisors of 7077)
...
7077 / 83 = 85.265060240964 (the remainder is 22, so 83 is not a divisor of 7077)
7077 / 84 = 84.25 (the remainder is 21, so 84 is not a divisor of 7077)