What are the divisors of 7025?

1, 5, 25, 281, 1405, 7025

There is a total of 6 positive divisors.
The sum of these divisors is 8742.
The arithmetic mean is 1457.

6 odd divisors

1, 5, 25, 281, 1405, 7025

How to compute the divisors of 7025?

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 7025 by each of the numbers from 1 to 7025 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)

7025 / 1 = 7025 (the remainder is 0, so 1 is a divisor of 7025)
7025 / 2 = 3512.5 (the remainder is 1, so 2 is not a divisor of 7025)
7025 / 3 = 2341.6666666667 (the remainder is 2, so 3 is not a divisor of 7025)
...
7025 / 7024 = 1.0001423690205 (the remainder is 1, so 7024 is not a divisor of 7025)
7025 / 7025 = 1 (the remainder is 0, so 7025 is a divisor of 7025)

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 7025 (i.e. 83.815273071201). 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 $\frac{N}{d} = D$ )

7025 / 1 = 7025 (the remainder is 0, so 1 and 7025 are divisors of 7025)
7025 / 2 = 3512.5 (the remainder is 1, so 2 is not a divisor of 7025)
7025 / 3 = 2341.6666666667 (the remainder is 2, so 3 is not a divisor of 7025)
...
7025 / 82 = 85.670731707317 (the remainder is 55, so 82 is not a divisor of 7025)
7025 / 83 = 84.638554216867 (the remainder is 53, so 83 is not a divisor of 7025)