What are the divisors of 3760?

1, 2, 4, 5, 8, 10, 16, 20, 40, 47, 80, 94, 188, 235, 376, 470, 752, 940, 1880, 3760

There is a total of 20 positive divisors.
The sum of these divisors is 8928.
The arithmetic mean is 446.4.

16 even divisors

2, 4, 8, 10, 16, 20, 40, 80, 94, 188, 376, 470, 752, 940, 1880, 3760

4 odd divisors

1, 5, 47, 235

How to compute the divisors of 3760?

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 3760 by each of the numbers from 1 to 3760 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)

3760 / 1 = 3760 (the remainder is 0, so 1 is a divisor of 3760)
3760 / 2 = 1880 (the remainder is 0, so 2 is a divisor of 3760)
3760 / 3 = 1253.3333333333 (the remainder is 1, so 3 is not a divisor of 3760)
...
3760 / 3759 = 1.000266028199 (the remainder is 1, so 3759 is not a divisor of 3760)
3760 / 3760 = 1 (the remainder is 0, so 3760 is a divisor of 3760)

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 3760 (i.e. 61.318838867024). 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 $\frac{N}{d} = D$ )

3760 / 1 = 3760 (the remainder is 0, so 1 and 3760 are divisors of 3760)
3760 / 2 = 1880 (the remainder is 0, so 2 and 1880 are divisors of 3760)
3760 / 3 = 1253.3333333333 (the remainder is 1, so 3 is not a divisor of 3760)
...
3760 / 60 = 62.666666666667 (the remainder is 40, so 60 is not a divisor of 3760)
3760 / 61 = 61.639344262295 (the remainder is 39, so 61 is not a divisor of 3760)