What are the divisors of 4904?

1, 2, 4, 8, 613, 1226, 2452, 4904

There is a total of 8 positive divisors.
The sum of these divisors is 9210.
The arithmetic mean is 1151.25.

6 even divisors

2, 4, 8, 1226, 2452, 4904

2 odd divisors

1, 613

How to compute the divisors of 4904?

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 4904 by each of the numbers from 1 to 4904 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)

4904 / 1 = 4904 (the remainder is 0, so 1 is a divisor of 4904)
4904 / 2 = 2452 (the remainder is 0, so 2 is a divisor of 4904)
4904 / 3 = 1634.6666666667 (the remainder is 2, so 3 is not a divisor of 4904)
...
4904 / 4903 = 1.0002039567612 (the remainder is 1, so 4903 is not a divisor of 4904)
4904 / 4904 = 1 (the remainder is 0, so 4904 is a divisor of 4904)

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 4904 (i.e. 70.028565600046). 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 $\frac{N}{d} = D$ )

4904 / 1 = 4904 (the remainder is 0, so 1 and 4904 are divisors of 4904)
4904 / 2 = 2452 (the remainder is 0, so 2 and 2452 are divisors of 4904)
4904 / 3 = 1634.6666666667 (the remainder is 2, so 3 is not a divisor of 4904)
...
4904 / 69 = 71.072463768116 (the remainder is 5, so 69 is not a divisor of 4904)
4904 / 70 = 70.057142857143 (the remainder is 4, so 70 is not a divisor of 4904)