What are the divisors of 1775?

1, 5, 25, 71, 355, 1775

There is a total of 6 positive divisors.
The sum of these divisors is 2232.
The arithmetic mean is 372.

6 odd divisors

1, 5, 25, 71, 355, 1775

How to compute the divisors of 1775?

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 1775 by each of the numbers from 1 to 1775 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)

1775 / 1 = 1775 (the remainder is 0, so 1 is a divisor of 1775)
1775 / 2 = 887.5 (the remainder is 1, so 2 is not a divisor of 1775)
1775 / 3 = 591.66666666667 (the remainder is 2, so 3 is not a divisor of 1775)
...
1775 / 1774 = 1.0005636978579 (the remainder is 1, so 1774 is not a divisor of 1775)
1775 / 1775 = 1 (the remainder is 0, so 1775 is a divisor of 1775)

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 1775 (i.e. 42.130748865882). 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 $\frac{N}{d} = D$ )

1775 / 1 = 1775 (the remainder is 0, so 1 and 1775 are divisors of 1775)
1775 / 2 = 887.5 (the remainder is 1, so 2 is not a divisor of 1775)
1775 / 3 = 591.66666666667 (the remainder is 2, so 3 is not a divisor of 1775)
...
1775 / 41 = 43.292682926829 (the remainder is 12, so 41 is not a divisor of 1775)
1775 / 42 = 42.261904761905 (the remainder is 11, so 42 is not a divisor of 1775)