What are the divisors of 3775?

1, 5, 25, 151, 755, 3775

There is a total of 6 positive divisors.
The sum of these divisors is 4712.
The arithmetic mean is 785.33333333333.

6 odd divisors

1, 5, 25, 151, 755, 3775

How to compute the divisors of 3775?

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 3775 by each of the numbers from 1 to 3775 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)

3775 / 1 = 3775 (the remainder is 0, so 1 is a divisor of 3775)
3775 / 2 = 1887.5 (the remainder is 1, so 2 is not a divisor of 3775)
3775 / 3 = 1258.3333333333 (the remainder is 1, so 3 is not a divisor of 3775)
...
3775 / 3774 = 1.0002649708532 (the remainder is 1, so 3774 is not a divisor of 3775)
3775 / 3775 = 1 (the remainder is 0, so 3775 is a divisor of 3775)

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 3775 (i.e. 61.441028637223). 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 $\frac{N}{d} = D$ )

3775 / 1 = 3775 (the remainder is 0, so 1 and 3775 are divisors of 3775)
3775 / 2 = 1887.5 (the remainder is 1, so 2 is not a divisor of 3775)
3775 / 3 = 1258.3333333333 (the remainder is 1, so 3 is not a divisor of 3775)
...
3775 / 60 = 62.916666666667 (the remainder is 55, so 60 is not a divisor of 3775)
3775 / 61 = 61.885245901639 (the remainder is 54, so 61 is not a divisor of 3775)