What are the divisors of 3737?

1, 37, 101, 3737

There is a total of 4 positive divisors.
The sum of these divisors is 3876.
The arithmetic mean is 969.

4 odd divisors

1, 37, 101, 3737

How to compute the divisors of 3737?

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 3737 by each of the numbers from 1 to 3737 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)

3737 / 1 = 3737 (the remainder is 0, so 1 is a divisor of 3737)
3737 / 2 = 1868.5 (the remainder is 1, so 2 is not a divisor of 3737)
3737 / 3 = 1245.6666666667 (the remainder is 2, so 3 is not a divisor of 3737)
...
3737 / 3736 = 1.0002676659529 (the remainder is 1, so 3736 is not a divisor of 3737)
3737 / 3737 = 1 (the remainder is 0, so 3737 is a divisor of 3737)

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 3737 (i.e. 61.131006862312). 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 $\frac{N}{d} = D$ )

3737 / 1 = 3737 (the remainder is 0, so 1 and 3737 are divisors of 3737)
3737 / 2 = 1868.5 (the remainder is 1, so 2 is not a divisor of 3737)
3737 / 3 = 1245.6666666667 (the remainder is 2, so 3 is not a divisor of 3737)
...
3737 / 60 = 62.283333333333 (the remainder is 17, so 60 is not a divisor of 3737)
3737 / 61 = 61.262295081967 (the remainder is 16, so 61 is not a divisor of 3737)