What are the divisors of 3770?

1, 2, 5, 10, 13, 26, 29, 58, 65, 130, 145, 290, 377, 754, 1885, 3770

There is a total of 16 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 472.5.

8 even divisors

2, 10, 26, 58, 130, 290, 754, 3770

8 odd divisors

1, 5, 13, 29, 65, 145, 377, 1885

How to compute the divisors of 3770?

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 3770 by each of the numbers from 1 to 3770 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)

3770 / 1 = 3770 (the remainder is 0, so 1 is a divisor of 3770)
3770 / 2 = 1885 (the remainder is 0, so 2 is a divisor of 3770)
3770 / 3 = 1256.6666666667 (the remainder is 2, so 3 is not a divisor of 3770)
...
3770 / 3769 = 1.0002653223667 (the remainder is 1, so 3769 is not a divisor of 3770)
3770 / 3770 = 1 (the remainder is 0, so 3770 is a divisor of 3770)

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 3770 (i.e. 61.400325732035). 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 $\frac{N}{d} = D$ )

3770 / 1 = 3770 (the remainder is 0, so 1 and 3770 are divisors of 3770)
3770 / 2 = 1885 (the remainder is 0, so 2 and 1885 are divisors of 3770)
3770 / 3 = 1256.6666666667 (the remainder is 2, so 3 is not a divisor of 3770)
...
3770 / 60 = 62.833333333333 (the remainder is 50, so 60 is not a divisor of 3770)
3770 / 61 = 61.803278688525 (the remainder is 49, so 61 is not a divisor of 3770)