What are the divisors of 2752?

1, 2, 4, 8, 16, 32, 43, 64, 86, 172, 344, 688, 1376, 2752

There is a total of 14 positive divisors.
The sum of these divisors is 5588.
The arithmetic mean is 399.14285714286.

12 even divisors

2, 4, 8, 16, 32, 64, 86, 172, 344, 688, 1376, 2752

2 odd divisors

1, 43

How to compute the divisors of 2752?

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 2752 by each of the numbers from 1 to 2752 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)

2752 / 1 = 2752 (the remainder is 0, so 1 is a divisor of 2752)
2752 / 2 = 1376 (the remainder is 0, so 2 is a divisor of 2752)
2752 / 3 = 917.33333333333 (the remainder is 1, so 3 is not a divisor of 2752)
...
2752 / 2751 = 1.0003635041803 (the remainder is 1, so 2751 is not a divisor of 2752)
2752 / 2752 = 1 (the remainder is 0, so 2752 is a divisor of 2752)

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 2752 (i.e. 52.459508194416). 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 $\frac{N}{d} = D$ )

2752 / 1 = 2752 (the remainder is 0, so 1 and 2752 are divisors of 2752)
2752 / 2 = 1376 (the remainder is 0, so 2 and 1376 are divisors of 2752)
2752 / 3 = 917.33333333333 (the remainder is 1, so 3 is not a divisor of 2752)
...
2752 / 51 = 53.960784313725 (the remainder is 49, so 51 is not a divisor of 2752)
2752 / 52 = 52.923076923077 (the remainder is 48, so 52 is not a divisor of 2752)