What are the divisors of 3177?

1, 3, 9, 353, 1059, 3177

There is a total of 6 positive divisors.
The sum of these divisors is 4602.
The arithmetic mean is 767.

6 odd divisors

1, 3, 9, 353, 1059, 3177

How to compute the divisors of 3177?

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 3177 by each of the numbers from 1 to 3177 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)

3177 / 1 = 3177 (the remainder is 0, so 1 is a divisor of 3177)
3177 / 2 = 1588.5 (the remainder is 1, so 2 is not a divisor of 3177)
3177 / 3 = 1059 (the remainder is 0, so 3 is a divisor of 3177)
...
3177 / 3176 = 1.000314861461 (the remainder is 1, so 3176 is not a divisor of 3177)
3177 / 3177 = 1 (the remainder is 0, so 3177 is a divisor of 3177)

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 3177 (i.e. 56.364882684168). 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 $\frac{N}{d} = D$ )

3177 / 1 = 3177 (the remainder is 0, so 1 and 3177 are divisors of 3177)
3177 / 2 = 1588.5 (the remainder is 1, so 2 is not a divisor of 3177)
3177 / 3 = 1059 (the remainder is 0, so 3 and 1059 are divisors of 3177)
...
3177 / 55 = 57.763636363636 (the remainder is 42, so 55 is not a divisor of 3177)
3177 / 56 = 56.732142857143 (the remainder is 41, so 56 is not a divisor of 3177)