What are the divisors of 797?

1, 797

There is a total of 2 positive divisors.
The sum of these divisors is 798.
The arithmetic mean is 399.

2 odd divisors

1, 797

How to compute the divisors of 797?

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 797 by each of the numbers from 1 to 797 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)

797 / 1 = 797 (the remainder is 0, so 1 is a divisor of 797)
797 / 2 = 398.5 (the remainder is 1, so 2 is not a divisor of 797)
797 / 3 = 265.66666666667 (the remainder is 2, so 3 is not a divisor of 797)
...
797 / 796 = 1.001256281407 (the remainder is 1, so 796 is not a divisor of 797)
797 / 797 = 1 (the remainder is 0, so 797 is a divisor of 797)

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 797 (i.e. 28.231188426986). 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 $\frac{N}{d} = D$ )

797 / 1 = 797 (the remainder is 0, so 1 and 797 are divisors of 797)
797 / 2 = 398.5 (the remainder is 1, so 2 is not a divisor of 797)
797 / 3 = 265.66666666667 (the remainder is 2, so 3 is not a divisor of 797)
...
797 / 27 = 29.518518518519 (the remainder is 14, so 27 is not a divisor of 797)
797 / 28 = 28.464285714286 (the remainder is 13, so 28 is not a divisor of 797)