What are the divisors of 2960?

1, 2, 4, 5, 8, 10, 16, 20, 37, 40, 74, 80, 148, 185, 296, 370, 592, 740, 1480, 2960

There is a total of 20 positive divisors.
The sum of these divisors is 7068.
The arithmetic mean is 353.4.

16 even divisors

2, 4, 8, 10, 16, 20, 40, 74, 80, 148, 296, 370, 592, 740, 1480, 2960

4 odd divisors

1, 5, 37, 185

How to compute the divisors of 2960?

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 2960 by each of the numbers from 1 to 2960 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)

2960 / 1 = 2960 (the remainder is 0, so 1 is a divisor of 2960)
2960 / 2 = 1480 (the remainder is 0, so 2 is a divisor of 2960)
2960 / 3 = 986.66666666667 (the remainder is 2, so 3 is not a divisor of 2960)
...
2960 / 2959 = 1.0003379520108 (the remainder is 1, so 2959 is not a divisor of 2960)
2960 / 2960 = 1 (the remainder is 0, so 2960 is a divisor of 2960)

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 2960 (i.e. 54.405882034942). 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 $\frac{N}{d} = D$ )

2960 / 1 = 2960 (the remainder is 0, so 1 and 2960 are divisors of 2960)
2960 / 2 = 1480 (the remainder is 0, so 2 and 1480 are divisors of 2960)
2960 / 3 = 986.66666666667 (the remainder is 2, so 3 is not a divisor of 2960)
...
2960 / 53 = 55.849056603774 (the remainder is 45, so 53 is not a divisor of 2960)
2960 / 54 = 54.814814814815 (the remainder is 44, so 54 is not a divisor of 2960)