What are the divisors of 4048?

1, 2, 4, 8, 11, 16, 22, 23, 44, 46, 88, 92, 176, 184, 253, 368, 506, 1012, 2024, 4048

There is a total of 20 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 446.4.

16 even divisors

2, 4, 8, 16, 22, 44, 46, 88, 92, 176, 184, 368, 506, 1012, 2024, 4048

4 odd divisors

1, 11, 23, 253

How to compute the divisors of 4048?

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 4048 by each of the numbers from 1 to 4048 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)

4048 / 1 = 4048 (the remainder is 0, so 1 is a divisor of 4048)
4048 / 2 = 2024 (the remainder is 0, so 2 is a divisor of 4048)
4048 / 3 = 1349.3333333333 (the remainder is 1, so 3 is not a divisor of 4048)
...
4048 / 4047 = 1.0002470966148 (the remainder is 1, so 4047 is not a divisor of 4048)
4048 / 4048 = 1 (the remainder is 0, so 4048 is a divisor of 4048)

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 4048 (i.e. 63.623894882347). 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 $\frac{N}{d} = D$ )

4048 / 1 = 4048 (the remainder is 0, so 1 and 4048 are divisors of 4048)
4048 / 2 = 2024 (the remainder is 0, so 2 and 2024 are divisors of 4048)
4048 / 3 = 1349.3333333333 (the remainder is 1, so 3 is not a divisor of 4048)
...
4048 / 62 = 65.290322580645 (the remainder is 18, so 62 is not a divisor of 4048)
4048 / 63 = 64.253968253968 (the remainder is 16, so 63 is not a divisor of 4048)