What are the divisors of 4928?

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 64, 77, 88, 112, 154, 176, 224, 308, 352, 448, 616, 704, 1232, 2464, 4928

There is a total of 28 positive divisors.
The sum of these divisors is 12192.
The arithmetic mean is 435.42857142857.

24 even divisors

2, 4, 8, 14, 16, 22, 28, 32, 44, 56, 64, 88, 112, 154, 176, 224, 308, 352, 448, 616, 704, 1232, 2464, 4928

4 odd divisors

1, 7, 11, 77

How to compute the divisors of 4928?

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 4928 by each of the numbers from 1 to 4928 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)

4928 / 1 = 4928 (the remainder is 0, so 1 is a divisor of 4928)
4928 / 2 = 2464 (the remainder is 0, so 2 is a divisor of 4928)
4928 / 3 = 1642.6666666667 (the remainder is 2, so 3 is not a divisor of 4928)
...
4928 / 4927 = 1.0002029632636 (the remainder is 1, so 4927 is not a divisor of 4928)
4928 / 4928 = 1 (the remainder is 0, so 4928 is a divisor of 4928)

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 4928 (i.e. 70.199715099137). 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 $\frac{N}{d} = D$ )

4928 / 1 = 4928 (the remainder is 0, so 1 and 4928 are divisors of 4928)
4928 / 2 = 2464 (the remainder is 0, so 2 and 2464 are divisors of 4928)
4928 / 3 = 1642.6666666667 (the remainder is 2, so 3 is not a divisor of 4928)
...
4928 / 69 = 71.420289855072 (the remainder is 29, so 69 is not a divisor of 4928)
4928 / 70 = 70.4 (the remainder is 28, so 70 is not a divisor of 4928)