What are the divisors of 1976?

1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 247, 494, 988, 1976

There is a total of 16 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 262.5.

12 even divisors

2, 4, 8, 26, 38, 52, 76, 104, 152, 494, 988, 1976

4 odd divisors

1, 13, 19, 247

How to compute the divisors of 1976?

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 1976 by each of the numbers from 1 to 1976 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)

1976 / 1 = 1976 (the remainder is 0, so 1 is a divisor of 1976)
1976 / 2 = 988 (the remainder is 0, so 2 is a divisor of 1976)
1976 / 3 = 658.66666666667 (the remainder is 2, so 3 is not a divisor of 1976)
...
1976 / 1975 = 1.0005063291139 (the remainder is 1, so 1975 is not a divisor of 1976)
1976 / 1976 = 1 (the remainder is 0, so 1976 is a divisor of 1976)

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 1976 (i.e. 44.452221541786). 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 $\frac{N}{d} = D$ )

1976 / 1 = 1976 (the remainder is 0, so 1 and 1976 are divisors of 1976)
1976 / 2 = 988 (the remainder is 0, so 2 and 988 are divisors of 1976)
1976 / 3 = 658.66666666667 (the remainder is 2, so 3 is not a divisor of 1976)
...
1976 / 43 = 45.953488372093 (the remainder is 41, so 43 is not a divisor of 1976)
1976 / 44 = 44.909090909091 (the remainder is 40, so 44 is not a divisor of 1976)