What are the divisors of 4960?

1, 2, 4, 5, 8, 10, 16, 20, 31, 32, 40, 62, 80, 124, 155, 160, 248, 310, 496, 620, 992, 1240, 2480, 4960

There is a total of 24 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 504.

20 even divisors

2, 4, 8, 10, 16, 20, 32, 40, 62, 80, 124, 160, 248, 310, 496, 620, 992, 1240, 2480, 4960

4 odd divisors

1, 5, 31, 155

How to compute the divisors of 4960?

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 4960 by each of the numbers from 1 to 4960 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)

4960 / 1 = 4960 (the remainder is 0, so 1 is a divisor of 4960)
4960 / 2 = 2480 (the remainder is 0, so 2 is a divisor of 4960)
4960 / 3 = 1653.3333333333 (the remainder is 1, so 3 is not a divisor of 4960)
...
4960 / 4959 = 1.0002016535592 (the remainder is 1, so 4959 is not a divisor of 4960)
4960 / 4960 = 1 (the remainder is 0, so 4960 is a divisor of 4960)

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 4960 (i.e. 70.427267446636). 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 $\frac{N}{d} = D$ )

4960 / 1 = 4960 (the remainder is 0, so 1 and 4960 are divisors of 4960)
4960 / 2 = 2480 (the remainder is 0, so 2 and 2480 are divisors of 4960)
4960 / 3 = 1653.3333333333 (the remainder is 1, so 3 is not a divisor of 4960)
...
4960 / 69 = 71.884057971014 (the remainder is 61, so 69 is not a divisor of 4960)
4960 / 70 = 70.857142857143 (the remainder is 60, so 70 is not a divisor of 4960)