What are the divisors of 760?

1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760

There is a total of 16 positive divisors.
The sum of these divisors is 1800.
The arithmetic mean is 112.5.

12 even divisors

2, 4, 8, 10, 20, 38, 40, 76, 152, 190, 380, 760

4 odd divisors

1, 5, 19, 95

How to compute the divisors of 760?

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 760 by each of the numbers from 1 to 760 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)

760 / 1 = 760 (the remainder is 0, so 1 is a divisor of 760)
760 / 2 = 380 (the remainder is 0, so 2 is a divisor of 760)
760 / 3 = 253.33333333333 (the remainder is 1, so 3 is not a divisor of 760)
...
760 / 759 = 1.0013175230567 (the remainder is 1, so 759 is not a divisor of 760)
760 / 760 = 1 (the remainder is 0, so 760 is a divisor of 760)

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 760 (i.e. 27.56809750418). 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 $\frac{N}{d} = D$ )

760 / 1 = 760 (the remainder is 0, so 1 and 760 are divisors of 760)
760 / 2 = 380 (the remainder is 0, so 2 and 380 are divisors of 760)
760 / 3 = 253.33333333333 (the remainder is 1, so 3 is not a divisor of 760)
...
760 / 26 = 29.230769230769 (the remainder is 6, so 26 is not a divisor of 760)
760 / 27 = 28.148148148148 (the remainder is 4, so 27 is not a divisor of 760)