What are the divisors of 2928?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 61, 122, 183, 244, 366, 488, 732, 976, 1464, 2928

There is a total of 20 positive divisors.
The sum of these divisors is 7688.
The arithmetic mean is 384.4.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 122, 244, 366, 488, 732, 976, 1464, 2928

4 odd divisors

1, 3, 61, 183

How to compute the divisors of 2928?

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 2928 by each of the numbers from 1 to 2928 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)

2928 / 1 = 2928 (the remainder is 0, so 1 is a divisor of 2928)
2928 / 2 = 1464 (the remainder is 0, so 2 is a divisor of 2928)
2928 / 3 = 976 (the remainder is 0, so 3 is a divisor of 2928)
...
2928 / 2927 = 1.0003416467373 (the remainder is 1, so 2927 is not a divisor of 2928)
2928 / 2928 = 1 (the remainder is 0, so 2928 is a divisor of 2928)

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 2928 (i.e. 54.110997033875). 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 $\frac{N}{d} = D$ )

2928 / 1 = 2928 (the remainder is 0, so 1 and 2928 are divisors of 2928)
2928 / 2 = 1464 (the remainder is 0, so 2 and 1464 are divisors of 2928)
2928 / 3 = 976 (the remainder is 0, so 3 and 976 are divisors of 2928)
...
2928 / 53 = 55.245283018868 (the remainder is 13, so 53 is not a divisor of 2928)
2928 / 54 = 54.222222222222 (the remainder is 12, so 54 is not a divisor of 2928)