What are the divisors of 770?

1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770

There is a total of 16 positive divisors.
The sum of these divisors is 1728.
The arithmetic mean is 108.

8 even divisors

2, 10, 14, 22, 70, 110, 154, 770

8 odd divisors

1, 5, 7, 11, 35, 55, 77, 385

How to compute the divisors of 770?

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 770 by each of the numbers from 1 to 770 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)

770 / 1 = 770 (the remainder is 0, so 1 is a divisor of 770)
770 / 2 = 385 (the remainder is 0, so 2 is a divisor of 770)
770 / 3 = 256.66666666667 (the remainder is 2, so 3 is not a divisor of 770)
...
770 / 769 = 1.001300390117 (the remainder is 1, so 769 is not a divisor of 770)
770 / 770 = 1 (the remainder is 0, so 770 is a divisor of 770)

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 770 (i.e. 27.748873851023). 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 $\frac{N}{d} = D$ )

770 / 1 = 770 (the remainder is 0, so 1 and 770 are divisors of 770)
770 / 2 = 385 (the remainder is 0, so 2 and 385 are divisors of 770)
770 / 3 = 256.66666666667 (the remainder is 2, so 3 is not a divisor of 770)
...
770 / 26 = 29.615384615385 (the remainder is 16, so 26 is not a divisor of 770)
770 / 27 = 28.518518518519 (the remainder is 14, so 27 is not a divisor of 770)