What are the divisors of 2775?

1, 3, 5, 15, 25, 37, 75, 111, 185, 555, 925, 2775

There is a total of 12 positive divisors.
The sum of these divisors is 4712.
The arithmetic mean is 392.66666666667.

12 odd divisors

1, 3, 5, 15, 25, 37, 75, 111, 185, 555, 925, 2775

How to compute the divisors of 2775?

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 2775 by each of the numbers from 1 to 2775 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)

2775 / 1 = 2775 (the remainder is 0, so 1 is a divisor of 2775)
2775 / 2 = 1387.5 (the remainder is 1, so 2 is not a divisor of 2775)
2775 / 3 = 925 (the remainder is 0, so 3 is a divisor of 2775)
...
2775 / 2774 = 1.0003604902668 (the remainder is 1, so 2774 is not a divisor of 2775)
2775 / 2775 = 1 (the remainder is 0, so 2775 is a divisor of 2775)

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 2775 (i.e. 52.678268764264). 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 $\frac{N}{d} = D$ )

2775 / 1 = 2775 (the remainder is 0, so 1 and 2775 are divisors of 2775)
2775 / 2 = 1387.5 (the remainder is 1, so 2 is not a divisor of 2775)
2775 / 3 = 925 (the remainder is 0, so 3 and 925 are divisors of 2775)
...
2775 / 51 = 54.411764705882 (the remainder is 21, so 51 is not a divisor of 2775)
2775 / 52 = 53.365384615385 (the remainder is 19, so 52 is not a divisor of 2775)