What are the divisors of 4850?

1, 2, 5, 10, 25, 50, 97, 194, 485, 970, 2425, 4850

There is a total of 12 positive divisors.
The sum of these divisors is 9114.
The arithmetic mean is 759.5.

6 even divisors

2, 10, 50, 194, 970, 4850

6 odd divisors

1, 5, 25, 97, 485, 2425

How to compute the divisors of 4850?

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 4850 by each of the numbers from 1 to 4850 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)

4850 / 1 = 4850 (the remainder is 0, so 1 is a divisor of 4850)
4850 / 2 = 2425 (the remainder is 0, so 2 is a divisor of 4850)
4850 / 3 = 1616.6666666667 (the remainder is 2, so 3 is not a divisor of 4850)
...
4850 / 4849 = 1.0002062280883 (the remainder is 1, so 4849 is not a divisor of 4850)
4850 / 4850 = 1 (the remainder is 0, so 4850 is a divisor of 4850)

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 4850 (i.e. 69.641941385921). 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 $\frac{N}{d} = D$ )

4850 / 1 = 4850 (the remainder is 0, so 1 and 4850 are divisors of 4850)
4850 / 2 = 2425 (the remainder is 0, so 2 and 2425 are divisors of 4850)
4850 / 3 = 1616.6666666667 (the remainder is 2, so 3 is not a divisor of 4850)
...
4850 / 68 = 71.323529411765 (the remainder is 22, so 68 is not a divisor of 4850)
4850 / 69 = 70.289855072464 (the remainder is 20, so 69 is not a divisor of 4850)