What are the divisors of 2177?

1, 7, 311, 2177

There is a total of 4 positive divisors.
The sum of these divisors is 2496.
The arithmetic mean is 624.

4 odd divisors

1, 7, 311, 2177

How to compute the divisors of 2177?

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 2177 by each of the numbers from 1 to 2177 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)

2177 / 1 = 2177 (the remainder is 0, so 1 is a divisor of 2177)
2177 / 2 = 1088.5 (the remainder is 1, so 2 is not a divisor of 2177)
2177 / 3 = 725.66666666667 (the remainder is 2, so 3 is not a divisor of 2177)
...
2177 / 2176 = 1.0004595588235 (the remainder is 1, so 2176 is not a divisor of 2177)
2177 / 2177 = 1 (the remainder is 0, so 2177 is a divisor of 2177)

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 2177 (i.e. 46.658332589153). 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 $\frac{N}{d} = D$ )

2177 / 1 = 2177 (the remainder is 0, so 1 and 2177 are divisors of 2177)
2177 / 2 = 1088.5 (the remainder is 1, so 2 is not a divisor of 2177)
2177 / 3 = 725.66666666667 (the remainder is 2, so 3 is not a divisor of 2177)
...
2177 / 45 = 48.377777777778 (the remainder is 17, so 45 is not a divisor of 2177)
2177 / 46 = 47.326086956522 (the remainder is 15, so 46 is not a divisor of 2177)