What are the divisors of 4174?

1, 2, 2087, 4174

There is a total of 4 positive divisors.
The sum of these divisors is 6264.
The arithmetic mean is 1566.

2 even divisors

2, 4174

2 odd divisors

1, 2087

How to compute the divisors of 4174?

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 4174 by each of the numbers from 1 to 4174 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)

4174 / 1 = 4174 (the remainder is 0, so 1 is a divisor of 4174)
4174 / 2 = 2087 (the remainder is 0, so 2 is a divisor of 4174)
4174 / 3 = 1391.3333333333 (the remainder is 1, so 3 is not a divisor of 4174)
...
4174 / 4173 = 1.0002396357537 (the remainder is 1, so 4173 is not a divisor of 4174)
4174 / 4174 = 1 (the remainder is 0, so 4174 is a divisor of 4174)

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 4174 (i.e. 64.606501220852). 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 $\frac{N}{d} = D$ )

4174 / 1 = 4174 (the remainder is 0, so 1 and 4174 are divisors of 4174)
4174 / 2 = 2087 (the remainder is 0, so 2 and 2087 are divisors of 4174)
4174 / 3 = 1391.3333333333 (the remainder is 1, so 3 is not a divisor of 4174)
...
4174 / 63 = 66.253968253968 (the remainder is 16, so 63 is not a divisor of 4174)
4174 / 64 = 65.21875 (the remainder is 14, so 64 is not a divisor of 4174)