What are the divisors of 773?

1, 773

There is a total of 2 positive divisors.
The sum of these divisors is 774.
The arithmetic mean is 387.

2 odd divisors

1, 773

How to compute the divisors of 773?

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 773 by each of the numbers from 1 to 773 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)

773 / 1 = 773 (the remainder is 0, so 1 is a divisor of 773)
773 / 2 = 386.5 (the remainder is 1, so 2 is not a divisor of 773)
773 / 3 = 257.66666666667 (the remainder is 2, so 3 is not a divisor of 773)
...
773 / 772 = 1.0012953367876 (the remainder is 1, so 772 is not a divisor of 773)
773 / 773 = 1 (the remainder is 0, so 773 is a divisor of 773)

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 773 (i.e. 27.802877548916). 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 $\frac{N}{d} = D$ )

773 / 1 = 773 (the remainder is 0, so 1 and 773 are divisors of 773)
773 / 2 = 386.5 (the remainder is 1, so 2 is not a divisor of 773)
773 / 3 = 257.66666666667 (the remainder is 2, so 3 is not a divisor of 773)
...
773 / 26 = 29.730769230769 (the remainder is 19, so 26 is not a divisor of 773)
773 / 27 = 28.62962962963 (the remainder is 17, so 27 is not a divisor of 773)