What are the divisors of 3763?

1, 53, 71, 3763

There is a total of 4 positive divisors.
The sum of these divisors is 3888.
The arithmetic mean is 972.

4 odd divisors

1, 53, 71, 3763

How to compute the divisors of 3763?

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 3763 by each of the numbers from 1 to 3763 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)

3763 / 1 = 3763 (the remainder is 0, so 1 is a divisor of 3763)
3763 / 2 = 1881.5 (the remainder is 1, so 2 is not a divisor of 3763)
3763 / 3 = 1254.3333333333 (the remainder is 1, so 3 is not a divisor of 3763)
...
3763 / 3762 = 1.0002658160553 (the remainder is 1, so 3762 is not a divisor of 3763)
3763 / 3763 = 1 (the remainder is 0, so 3763 is a divisor of 3763)

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 3763 (i.e. 61.34329629226). 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 $\frac{N}{d} = D$ )

3763 / 1 = 3763 (the remainder is 0, so 1 and 3763 are divisors of 3763)
3763 / 2 = 1881.5 (the remainder is 1, so 2 is not a divisor of 3763)
3763 / 3 = 1254.3333333333 (the remainder is 1, so 3 is not a divisor of 3763)
...
3763 / 60 = 62.716666666667 (the remainder is 43, so 60 is not a divisor of 3763)
3763 / 61 = 61.688524590164 (the remainder is 42, so 61 is not a divisor of 3763)