What are the divisors of 4849?

1, 13, 373, 4849

There is a total of 4 positive divisors.
The sum of these divisors is 5236.
The arithmetic mean is 1309.

4 odd divisors

1, 13, 373, 4849

How to compute the divisors of 4849?

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 4849 by each of the numbers from 1 to 4849 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)

4849 / 1 = 4849 (the remainder is 0, so 1 is a divisor of 4849)
4849 / 2 = 2424.5 (the remainder is 1, so 2 is not a divisor of 4849)
4849 / 3 = 1616.3333333333 (the remainder is 1, so 3 is not a divisor of 4849)
...
4849 / 4848 = 1.0002062706271 (the remainder is 1, so 4848 is not a divisor of 4849)
4849 / 4849 = 1 (the remainder is 0, so 4849 is a divisor of 4849)

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 4849 (i.e. 69.634761434215). 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 $\frac{N}{d} = D$ )

4849 / 1 = 4849 (the remainder is 0, so 1 and 4849 are divisors of 4849)
4849 / 2 = 2424.5 (the remainder is 1, so 2 is not a divisor of 4849)
4849 / 3 = 1616.3333333333 (the remainder is 1, so 3 is not a divisor of 4849)
...
4849 / 68 = 71.308823529412 (the remainder is 21, so 68 is not a divisor of 4849)
4849 / 69 = 70.275362318841 (the remainder is 19, so 69 is not a divisor of 4849)