What are the divisors of 4640?

1, 2, 4, 5, 8, 10, 16, 20, 29, 32, 40, 58, 80, 116, 145, 160, 232, 290, 464, 580, 928, 1160, 2320, 4640

There is a total of 24 positive divisors.
The sum of these divisors is 11340.
The arithmetic mean is 472.5.

20 even divisors

2, 4, 8, 10, 16, 20, 32, 40, 58, 80, 116, 160, 232, 290, 464, 580, 928, 1160, 2320, 4640

4 odd divisors

1, 5, 29, 145

How to compute the divisors of 4640?

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 4640 by each of the numbers from 1 to 4640 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)

4640 / 1 = 4640 (the remainder is 0, so 1 is a divisor of 4640)
4640 / 2 = 2320 (the remainder is 0, so 2 is a divisor of 4640)
4640 / 3 = 1546.6666666667 (the remainder is 2, so 3 is not a divisor of 4640)
...
4640 / 4639 = 1.0002155636991 (the remainder is 1, so 4639 is not a divisor of 4640)
4640 / 4640 = 1 (the remainder is 0, so 4640 is a divisor of 4640)

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 4640 (i.e. 68.117545463706). 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 $\frac{N}{d} = D$ )

4640 / 1 = 4640 (the remainder is 0, so 1 and 4640 are divisors of 4640)
4640 / 2 = 2320 (the remainder is 0, so 2 and 2320 are divisors of 4640)
4640 / 3 = 1546.6666666667 (the remainder is 2, so 3 is not a divisor of 4640)
...
4640 / 67 = 69.253731343284 (the remainder is 17, so 67 is not a divisor of 4640)
4640 / 68 = 68.235294117647 (the remainder is 16, so 68 is not a divisor of 4640)