What are the divisors of 4888?

1, 2, 4, 8, 13, 26, 47, 52, 94, 104, 188, 376, 611, 1222, 2444, 4888

There is a total of 16 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 630.

12 even divisors

2, 4, 8, 26, 52, 94, 104, 188, 376, 1222, 2444, 4888

4 odd divisors

1, 13, 47, 611

How to compute the divisors of 4888?

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 4888 by each of the numbers from 1 to 4888 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)

4888 / 1 = 4888 (the remainder is 0, so 1 is a divisor of 4888)
4888 / 2 = 2444 (the remainder is 0, so 2 is a divisor of 4888)
4888 / 3 = 1629.3333333333 (the remainder is 1, so 3 is not a divisor of 4888)
...
4888 / 4887 = 1.000204624514 (the remainder is 1, so 4887 is not a divisor of 4888)
4888 / 4888 = 1 (the remainder is 0, so 4888 is a divisor of 4888)

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 4888 (i.e. 69.914233171794). 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 $\frac{N}{d} = D$ )

4888 / 1 = 4888 (the remainder is 0, so 1 and 4888 are divisors of 4888)
4888 / 2 = 2444 (the remainder is 0, so 2 and 2444 are divisors of 4888)
4888 / 3 = 1629.3333333333 (the remainder is 1, so 3 is not a divisor of 4888)
...
4888 / 68 = 71.882352941176 (the remainder is 60, so 68 is not a divisor of 4888)
4888 / 69 = 70.840579710145 (the remainder is 58, so 69 is not a divisor of 4888)