What are the divisors of 2174?

1, 2, 1087, 2174

There is a total of 4 positive divisors.
The sum of these divisors is 3264.
The arithmetic mean is 816.

2 even divisors

2, 2174

2 odd divisors

1, 1087

How to compute the divisors of 2174?

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 2174 by each of the numbers from 1 to 2174 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)

2174 / 1 = 2174 (the remainder is 0, so 1 is a divisor of 2174)
2174 / 2 = 1087 (the remainder is 0, so 2 is a divisor of 2174)
2174 / 3 = 724.66666666667 (the remainder is 2, so 3 is not a divisor of 2174)
...
2174 / 2173 = 1.0004601932812 (the remainder is 1, so 2173 is not a divisor of 2174)
2174 / 2174 = 1 (the remainder is 0, so 2174 is a divisor of 2174)

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 2174 (i.e. 46.626172907499). 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 $\frac{N}{d} = D$ )

2174 / 1 = 2174 (the remainder is 0, so 1 and 2174 are divisors of 2174)
2174 / 2 = 1087 (the remainder is 0, so 2 and 1087 are divisors of 2174)
2174 / 3 = 724.66666666667 (the remainder is 2, so 3 is not a divisor of 2174)
...
2174 / 45 = 48.311111111111 (the remainder is 14, so 45 is not a divisor of 2174)
2174 / 46 = 47.260869565217 (the remainder is 12, so 46 is not a divisor of 2174)