What are the divisors of 751?

1, 751

There is a total of 2 positive divisors.
The sum of these divisors is 752.
The arithmetic mean is 376.

2 odd divisors

1, 751

How to compute the divisors of 751?

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 751 by each of the numbers from 1 to 751 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)

751 / 1 = 751 (the remainder is 0, so 1 is a divisor of 751)
751 / 2 = 375.5 (the remainder is 1, so 2 is not a divisor of 751)
751 / 3 = 250.33333333333 (the remainder is 1, so 3 is not a divisor of 751)
...
751 / 750 = 1.0013333333333 (the remainder is 1, so 750 is not a divisor of 751)
751 / 751 = 1 (the remainder is 0, so 751 is a divisor of 751)

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 751 (i.e. 27.404379212089). 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 $\frac{N}{d} = D$ )

751 / 1 = 751 (the remainder is 0, so 1 and 751 are divisors of 751)
751 / 2 = 375.5 (the remainder is 1, so 2 is not a divisor of 751)
751 / 3 = 250.33333333333 (the remainder is 1, so 3 is not a divisor of 751)
...
751 / 26 = 28.884615384615 (the remainder is 23, so 26 is not a divisor of 751)
751 / 27 = 27.814814814815 (the remainder is 22, so 27 is not a divisor of 751)