What are the divisors of 2672?

1, 2, 4, 8, 16, 167, 334, 668, 1336, 2672

There is a total of 10 positive divisors.
The sum of these divisors is 5208.
The arithmetic mean is 520.8.

8 even divisors

2, 4, 8, 16, 334, 668, 1336, 2672

2 odd divisors

1, 167

How to compute the divisors of 2672?

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 2672 by each of the numbers from 1 to 2672 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)

2672 / 1 = 2672 (the remainder is 0, so 1 is a divisor of 2672)
2672 / 2 = 1336 (the remainder is 0, so 2 is a divisor of 2672)
2672 / 3 = 890.66666666667 (the remainder is 2, so 3 is not a divisor of 2672)
...
2672 / 2671 = 1.0003743916136 (the remainder is 1, so 2671 is not a divisor of 2672)
2672 / 2672 = 1 (the remainder is 0, so 2672 is a divisor of 2672)

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 2672 (i.e. 51.69139193328). 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 $\frac{N}{d} = D$ )

2672 / 1 = 2672 (the remainder is 0, so 1 and 2672 are divisors of 2672)
2672 / 2 = 1336 (the remainder is 0, so 2 and 1336 are divisors of 2672)
2672 / 3 = 890.66666666667 (the remainder is 2, so 3 is not a divisor of 2672)
...
2672 / 50 = 53.44 (the remainder is 22, so 50 is not a divisor of 2672)
2672 / 51 = 52.392156862745 (the remainder is 20, so 51 is not a divisor of 2672)