What are the divisors of 1960?

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960

There is a total of 24 positive divisors.
The sum of these divisors is 5130.
The arithmetic mean is 213.75.

18 even divisors

2, 4, 8, 10, 14, 20, 28, 40, 56, 70, 98, 140, 196, 280, 392, 490, 980, 1960

6 odd divisors

1, 5, 7, 35, 49, 245

How to compute the divisors of 1960?

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 1960 by each of the numbers from 1 to 1960 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)

1960 / 1 = 1960 (the remainder is 0, so 1 is a divisor of 1960)
1960 / 2 = 980 (the remainder is 0, so 2 is a divisor of 1960)
1960 / 3 = 653.33333333333 (the remainder is 1, so 3 is not a divisor of 1960)
...
1960 / 1959 = 1.0005104645227 (the remainder is 1, so 1959 is not a divisor of 1960)
1960 / 1960 = 1 (the remainder is 0, so 1960 is a divisor of 1960)

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 1960 (i.e. 44.271887242357). 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 $\frac{N}{d} = D$ )

1960 / 1 = 1960 (the remainder is 0, so 1 and 1960 are divisors of 1960)
1960 / 2 = 980 (the remainder is 0, so 2 and 980 are divisors of 1960)
1960 / 3 = 653.33333333333 (the remainder is 1, so 3 is not a divisor of 1960)
...
1960 / 43 = 45.581395348837 (the remainder is 25, so 43 is not a divisor of 1960)
1960 / 44 = 44.545454545455 (the remainder is 24, so 44 is not a divisor of 1960)