What are the divisors of 4169?

1, 11, 379, 4169

There is a total of 4 positive divisors.
The sum of these divisors is 4560.
The arithmetic mean is 1140.

4 odd divisors

1, 11, 379, 4169

How to compute the divisors of 4169?

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 4169 by each of the numbers from 1 to 4169 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)

4169 / 1 = 4169 (the remainder is 0, so 1 is a divisor of 4169)
4169 / 2 = 2084.5 (the remainder is 1, so 2 is not a divisor of 4169)
4169 / 3 = 1389.6666666667 (the remainder is 2, so 3 is not a divisor of 4169)
...
4169 / 4168 = 1.0002399232246 (the remainder is 1, so 4168 is not a divisor of 4169)
4169 / 4169 = 1 (the remainder is 0, so 4169 is a divisor of 4169)

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 4169 (i.e. 64.567793829432). 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 $\frac{N}{d} = D$ )

4169 / 1 = 4169 (the remainder is 0, so 1 and 4169 are divisors of 4169)
4169 / 2 = 2084.5 (the remainder is 1, so 2 is not a divisor of 4169)
4169 / 3 = 1389.6666666667 (the remainder is 2, so 3 is not a divisor of 4169)
...
4169 / 63 = 66.174603174603 (the remainder is 11, so 63 is not a divisor of 4169)
4169 / 64 = 65.140625 (the remainder is 9, so 64 is not a divisor of 4169)