What are the divisors of 3850?

1, 2, 5, 7, 10, 11, 14, 22, 25, 35, 50, 55, 70, 77, 110, 154, 175, 275, 350, 385, 550, 770, 1925, 3850

There is a total of 24 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 372.

12 even divisors

2, 10, 14, 22, 50, 70, 110, 154, 350, 550, 770, 3850

12 odd divisors

1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925

How to compute the divisors of 3850?

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 3850 by each of the numbers from 1 to 3850 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)

3850 / 1 = 3850 (the remainder is 0, so 1 is a divisor of 3850)
3850 / 2 = 1925 (the remainder is 0, so 2 is a divisor of 3850)
3850 / 3 = 1283.3333333333 (the remainder is 1, so 3 is not a divisor of 3850)
...
3850 / 3849 = 1.0002598077423 (the remainder is 1, so 3849 is not a divisor of 3850)
3850 / 3850 = 1 (the remainder is 0, so 3850 is a divisor of 3850)

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 3850 (i.e. 62.048368229954). 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 $\frac{N}{d} = D$ )

3850 / 1 = 3850 (the remainder is 0, so 1 and 3850 are divisors of 3850)
3850 / 2 = 1925 (the remainder is 0, so 2 and 1925 are divisors of 3850)
3850 / 3 = 1283.3333333333 (the remainder is 1, so 3 is not a divisor of 3850)
...
3850 / 61 = 63.114754098361 (the remainder is 7, so 61 is not a divisor of 3850)
3850 / 62 = 62.096774193548 (the remainder is 6, so 62 is not a divisor of 3850)