What are the divisors of 755?

1, 5, 151, 755

There is a total of 4 positive divisors.
The sum of these divisors is 912.
The arithmetic mean is 228.

4 odd divisors

1, 5, 151, 755

How to compute the divisors of 755?

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 755 by each of the numbers from 1 to 755 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)

755 / 1 = 755 (the remainder is 0, so 1 is a divisor of 755)
755 / 2 = 377.5 (the remainder is 1, so 2 is not a divisor of 755)
755 / 3 = 251.66666666667 (the remainder is 2, so 3 is not a divisor of 755)
...
755 / 754 = 1.0013262599469 (the remainder is 1, so 754 is not a divisor of 755)
755 / 755 = 1 (the remainder is 0, so 755 is a divisor of 755)

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 755 (i.e. 27.477263328068). 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 $\frac{N}{d} = D$ )

755 / 1 = 755 (the remainder is 0, so 1 and 755 are divisors of 755)
755 / 2 = 377.5 (the remainder is 1, so 2 is not a divisor of 755)
755 / 3 = 251.66666666667 (the remainder is 2, so 3 is not a divisor of 755)
...
755 / 26 = 29.038461538462 (the remainder is 1, so 26 is not a divisor of 755)
755 / 27 = 27.962962962963 (the remainder is 26, so 27 is not a divisor of 755)