What are the divisors of 1925?

1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925

There is a total of 12 positive divisors.
The sum of these divisors is 2976.
The arithmetic mean is 248.

12 odd divisors

1, 5, 7, 11, 25, 35, 55, 77, 175, 275, 385, 1925

How to compute the divisors of 1925?

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 1925 by each of the numbers from 1 to 1925 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)

1925 / 1 = 1925 (the remainder is 0, so 1 is a divisor of 1925)
1925 / 2 = 962.5 (the remainder is 1, so 2 is not a divisor of 1925)
1925 / 3 = 641.66666666667 (the remainder is 2, so 3 is not a divisor of 1925)
...
1925 / 1924 = 1.0005197505198 (the remainder is 1, so 1924 is not a divisor of 1925)
1925 / 1925 = 1 (the remainder is 0, so 1925 is a divisor of 1925)

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 1925 (i.e. 43.874821936961). 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 $\frac{N}{d} = D$ )

1925 / 1 = 1925 (the remainder is 0, so 1 and 1925 are divisors of 1925)
1925 / 2 = 962.5 (the remainder is 1, so 2 is not a divisor of 1925)
1925 / 3 = 641.66666666667 (the remainder is 2, so 3 is not a divisor of 1925)
...
1925 / 42 = 45.833333333333 (the remainder is 35, so 42 is not a divisor of 1925)
1925 / 43 = 44.767441860465 (the remainder is 33, so 43 is not a divisor of 1925)