What are the divisors of 2670?

1, 2, 3, 5, 6, 10, 15, 30, 89, 178, 267, 445, 534, 890, 1335, 2670

There is a total of 16 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 405.

8 even divisors

2, 6, 10, 30, 178, 534, 890, 2670

8 odd divisors

1, 3, 5, 15, 89, 267, 445, 1335

How to compute the divisors of 2670?

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 2670 by each of the numbers from 1 to 2670 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)

2670 / 1 = 2670 (the remainder is 0, so 1 is a divisor of 2670)
2670 / 2 = 1335 (the remainder is 0, so 2 is a divisor of 2670)
2670 / 3 = 890 (the remainder is 0, so 3 is a divisor of 2670)
...
2670 / 2669 = 1.0003746721619 (the remainder is 1, so 2669 is not a divisor of 2670)
2670 / 2670 = 1 (the remainder is 0, so 2670 is a divisor of 2670)

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 2670 (i.e. 51.672042731055). 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 $\frac{N}{d} = D$ )

2670 / 1 = 2670 (the remainder is 0, so 1 and 2670 are divisors of 2670)
2670 / 2 = 1335 (the remainder is 0, so 2 and 1335 are divisors of 2670)
2670 / 3 = 890 (the remainder is 0, so 3 and 890 are divisors of 2670)
...
2670 / 50 = 53.4 (the remainder is 20, so 50 is not a divisor of 2670)
2670 / 51 = 52.352941176471 (the remainder is 18, so 51 is not a divisor of 2670)