What are the divisors of 752?

1, 2, 4, 8, 16, 47, 94, 188, 376, 752

There is a total of 10 positive divisors.
The sum of these divisors is 1488.
The arithmetic mean is 148.8.

8 even divisors

2, 4, 8, 16, 94, 188, 376, 752

2 odd divisors

1, 47

How to compute the divisors of 752?

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 752 by each of the numbers from 1 to 752 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)

752 / 1 = 752 (the remainder is 0, so 1 is a divisor of 752)
752 / 2 = 376 (the remainder is 0, so 2 is a divisor of 752)
752 / 3 = 250.66666666667 (the remainder is 2, so 3 is not a divisor of 752)
...
752 / 751 = 1.0013315579228 (the remainder is 1, so 751 is not a divisor of 752)
752 / 752 = 1 (the remainder is 0, so 752 is a divisor of 752)

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 752 (i.e. 27.422618401604). 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 $\frac{N}{d} = D$ )

752 / 1 = 752 (the remainder is 0, so 1 and 752 are divisors of 752)
752 / 2 = 376 (the remainder is 0, so 2 and 376 are divisors of 752)
752 / 3 = 250.66666666667 (the remainder is 2, so 3 is not a divisor of 752)
...
752 / 26 = 28.923076923077 (the remainder is 24, so 26 is not a divisor of 752)
752 / 27 = 27.851851851852 (the remainder is 23, so 27 is not a divisor of 752)