What are the divisors of 762?

1, 2, 3, 6, 127, 254, 381, 762

There is a total of 8 positive divisors.
The sum of these divisors is 1536.
The arithmetic mean is 192.

4 even divisors

2, 6, 254, 762

4 odd divisors

1, 3, 127, 381

How to compute the divisors of 762?

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 762 by each of the numbers from 1 to 762 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)

762 / 1 = 762 (the remainder is 0, so 1 is a divisor of 762)
762 / 2 = 381 (the remainder is 0, so 2 is a divisor of 762)
762 / 3 = 254 (the remainder is 0, so 3 is a divisor of 762)
...
762 / 761 = 1.0013140604468 (the remainder is 1, so 761 is not a divisor of 762)
762 / 762 = 1 (the remainder is 0, so 762 is a divisor of 762)

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 762 (i.e. 27.604347483685). 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 $\frac{N}{d} = D$ )

762 / 1 = 762 (the remainder is 0, so 1 and 762 are divisors of 762)
762 / 2 = 381 (the remainder is 0, so 2 and 381 are divisors of 762)
762 / 3 = 254 (the remainder is 0, so 3 and 254 are divisors of 762)
...
762 / 26 = 29.307692307692 (the remainder is 8, so 26 is not a divisor of 762)
762 / 27 = 28.222222222222 (the remainder is 6, so 27 is not a divisor of 762)