What are the divisors of 4925?

1, 5, 25, 197, 985, 4925

There is a total of 6 positive divisors.
The sum of these divisors is 6138.
The arithmetic mean is 1023.

6 odd divisors

1, 5, 25, 197, 985, 4925

How to compute the divisors of 4925?

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 4925 by each of the numbers from 1 to 4925 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)

4925 / 1 = 4925 (the remainder is 0, so 1 is a divisor of 4925)
4925 / 2 = 2462.5 (the remainder is 1, so 2 is not a divisor of 4925)
4925 / 3 = 1641.6666666667 (the remainder is 2, so 3 is not a divisor of 4925)
...
4925 / 4924 = 1.0002030869212 (the remainder is 1, so 4924 is not a divisor of 4925)
4925 / 4925 = 1 (the remainder is 0, so 4925 is a divisor of 4925)

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 4925 (i.e. 70.178344238091). 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 $\frac{N}{d} = D$ )

4925 / 1 = 4925 (the remainder is 0, so 1 and 4925 are divisors of 4925)
4925 / 2 = 2462.5 (the remainder is 1, so 2 is not a divisor of 4925)
4925 / 3 = 1641.6666666667 (the remainder is 2, so 3 is not a divisor of 4925)
...
4925 / 69 = 71.376811594203 (the remainder is 26, so 69 is not a divisor of 4925)
4925 / 70 = 70.357142857143 (the remainder is 25, so 70 is not a divisor of 4925)