What are the divisors of 1475?

1, 5, 25, 59, 295, 1475

There is a total of 6 positive divisors.
The sum of these divisors is 1860.
The arithmetic mean is 310.

6 odd divisors

1, 5, 25, 59, 295, 1475

How to compute the divisors of 1475?

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 1475 by each of the numbers from 1 to 1475 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)

1475 / 1 = 1475 (the remainder is 0, so 1 is a divisor of 1475)
1475 / 2 = 737.5 (the remainder is 1, so 2 is not a divisor of 1475)
1475 / 3 = 491.66666666667 (the remainder is 2, so 3 is not a divisor of 1475)
...
1475 / 1474 = 1.0006784260516 (the remainder is 1, so 1474 is not a divisor of 1475)
1475 / 1475 = 1 (the remainder is 0, so 1475 is a divisor of 1475)

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 1475 (i.e. 38.405728739343). 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 $\frac{N}{d} = D$ )

1475 / 1 = 1475 (the remainder is 0, so 1 and 1475 are divisors of 1475)
1475 / 2 = 737.5 (the remainder is 1, so 2 is not a divisor of 1475)
1475 / 3 = 491.66666666667 (the remainder is 2, so 3 is not a divisor of 1475)
...
1475 / 37 = 39.864864864865 (the remainder is 32, so 37 is not a divisor of 1475)
1475 / 38 = 38.815789473684 (the remainder is 31, so 38 is not a divisor of 1475)