What are the divisors of 1940?

1, 2, 4, 5, 10, 20, 97, 194, 388, 485, 970, 1940

There is a total of 12 positive divisors.
The sum of these divisors is 4116.
The arithmetic mean is 343.

8 even divisors

2, 4, 10, 20, 194, 388, 970, 1940

4 odd divisors

1, 5, 97, 485

How to compute the divisors of 1940?

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 1940 by each of the numbers from 1 to 1940 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)

1940 / 1 = 1940 (the remainder is 0, so 1 is a divisor of 1940)
1940 / 2 = 970 (the remainder is 0, so 2 is a divisor of 1940)
1940 / 3 = 646.66666666667 (the remainder is 2, so 3 is not a divisor of 1940)
...
1940 / 1939 = 1.0005157297576 (the remainder is 1, so 1939 is not a divisor of 1940)
1940 / 1940 = 1 (the remainder is 0, so 1940 is a divisor of 1940)

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 1940 (i.e. 44.04543109109). 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 $\frac{N}{d} = D$ )

1940 / 1 = 1940 (the remainder is 0, so 1 and 1940 are divisors of 1940)
1940 / 2 = 970 (the remainder is 0, so 2 and 970 are divisors of 1940)
1940 / 3 = 646.66666666667 (the remainder is 2, so 3 is not a divisor of 1940)
...
1940 / 43 = 45.116279069767 (the remainder is 5, so 43 is not a divisor of 1940)
1940 / 44 = 44.090909090909 (the remainder is 4, so 44 is not a divisor of 1940)