What are the divisors of 4672?

1, 2, 4, 8, 16, 32, 64, 73, 146, 292, 584, 1168, 2336, 4672

There is a total of 14 positive divisors.
The sum of these divisors is 9398.
The arithmetic mean is 671.28571428571.

12 even divisors

2, 4, 8, 16, 32, 64, 146, 292, 584, 1168, 2336, 4672

2 odd divisors

1, 73

How to compute the divisors of 4672?

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 4672 by each of the numbers from 1 to 4672 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)

4672 / 1 = 4672 (the remainder is 0, so 1 is a divisor of 4672)
4672 / 2 = 2336 (the remainder is 0, so 2 is a divisor of 4672)
4672 / 3 = 1557.3333333333 (the remainder is 1, so 3 is not a divisor of 4672)
...
4672 / 4671 = 1.0002140869193 (the remainder is 1, so 4671 is not a divisor of 4672)
4672 / 4672 = 1 (the remainder is 0, so 4672 is a divisor of 4672)

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 4672 (i.e. 68.35202996254). 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 $\frac{N}{d} = D$ )

4672 / 1 = 4672 (the remainder is 0, so 1 and 4672 are divisors of 4672)
4672 / 2 = 2336 (the remainder is 0, so 2 and 2336 are divisors of 4672)
4672 / 3 = 1557.3333333333 (the remainder is 1, so 3 is not a divisor of 4672)
...
4672 / 67 = 69.731343283582 (the remainder is 49, so 67 is not a divisor of 4672)
4672 / 68 = 68.705882352941 (the remainder is 48, so 68 is not a divisor of 4672)