What are the divisors of 3797?

1, 3797

There is a total of 2 positive divisors.
The sum of these divisors is 3798.
The arithmetic mean is 1899.

2 odd divisors

1, 3797

How to compute the divisors of 3797?

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 3797 by each of the numbers from 1 to 3797 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)

3797 / 1 = 3797 (the remainder is 0, so 1 is a divisor of 3797)
3797 / 2 = 1898.5 (the remainder is 1, so 2 is not a divisor of 3797)
3797 / 3 = 1265.6666666667 (the remainder is 2, so 3 is not a divisor of 3797)
...
3797 / 3796 = 1.0002634351949 (the remainder is 1, so 3796 is not a divisor of 3797)
3797 / 3797 = 1 (the remainder is 0, so 3797 is a divisor of 3797)

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 3797 (i.e. 61.619802012016). 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 $\frac{N}{d} = D$ )

3797 / 1 = 3797 (the remainder is 0, so 1 and 3797 are divisors of 3797)
3797 / 2 = 1898.5 (the remainder is 1, so 2 is not a divisor of 3797)
3797 / 3 = 1265.6666666667 (the remainder is 2, so 3 is not a divisor of 3797)
...
3797 / 60 = 63.283333333333 (the remainder is 17, so 60 is not a divisor of 3797)
3797 / 61 = 62.245901639344 (the remainder is 15, so 61 is not a divisor of 3797)