What are the divisors of 4150?

1, 2, 5, 10, 25, 50, 83, 166, 415, 830, 2075, 4150

There is a total of 12 positive divisors.
The sum of these divisors is 7812.
The arithmetic mean is 651.

6 even divisors

2, 10, 50, 166, 830, 4150

6 odd divisors

1, 5, 25, 83, 415, 2075

How to compute the divisors of 4150?

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 4150 by each of the numbers from 1 to 4150 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)

4150 / 1 = 4150 (the remainder is 0, so 1 is a divisor of 4150)
4150 / 2 = 2075 (the remainder is 0, so 2 is a divisor of 4150)
4150 / 3 = 1383.3333333333 (the remainder is 1, so 3 is not a divisor of 4150)
...
4150 / 4149 = 1.000241021933 (the remainder is 1, so 4149 is not a divisor of 4150)
4150 / 4150 = 1 (the remainder is 0, so 4150 is a divisor of 4150)

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 4150 (i.e. 64.420493633626). 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 $\frac{N}{d} = D$ )

4150 / 1 = 4150 (the remainder is 0, so 1 and 4150 are divisors of 4150)
4150 / 2 = 2075 (the remainder is 0, so 2 and 2075 are divisors of 4150)
4150 / 3 = 1383.3333333333 (the remainder is 1, so 3 is not a divisor of 4150)
...
4150 / 63 = 65.873015873016 (the remainder is 55, so 63 is not a divisor of 4150)
4150 / 64 = 64.84375 (the remainder is 54, so 64 is not a divisor of 4150)