What are the divisors of 4852?

1, 2, 4, 1213, 2426, 4852

There is a total of 6 positive divisors.
The sum of these divisors is 8498.
The arithmetic mean is 1416.3333333333.

4 even divisors

2, 4, 2426, 4852

2 odd divisors

1, 1213

How to compute the divisors of 4852?

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 4852 by each of the numbers from 1 to 4852 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)

4852 / 1 = 4852 (the remainder is 0, so 1 is a divisor of 4852)
4852 / 2 = 2426 (the remainder is 0, so 2 is a divisor of 4852)
4852 / 3 = 1617.3333333333 (the remainder is 1, so 3 is not a divisor of 4852)
...
4852 / 4851 = 1.0002061430633 (the remainder is 1, so 4851 is not a divisor of 4852)
4852 / 4852 = 1 (the remainder is 0, so 4852 is a divisor of 4852)

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 4852 (i.e. 69.656299069072). 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 $\frac{N}{d} = D$ )

4852 / 1 = 4852 (the remainder is 0, so 1 and 4852 are divisors of 4852)
4852 / 2 = 2426 (the remainder is 0, so 2 and 2426 are divisors of 4852)
4852 / 3 = 1617.3333333333 (the remainder is 1, so 3 is not a divisor of 4852)
...
4852 / 68 = 71.352941176471 (the remainder is 24, so 68 is not a divisor of 4852)
4852 / 69 = 70.31884057971 (the remainder is 22, so 69 is not a divisor of 4852)