What are the divisors of 4250?

1, 2, 5, 10, 17, 25, 34, 50, 85, 125, 170, 250, 425, 850, 2125, 4250

There is a total of 16 positive divisors.
The sum of these divisors is 8424.
The arithmetic mean is 526.5.

8 even divisors

2, 10, 34, 50, 170, 250, 850, 4250

8 odd divisors

1, 5, 17, 25, 85, 125, 425, 2125

How to compute the divisors of 4250?

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 4250 by each of the numbers from 1 to 4250 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)

4250 / 1 = 4250 (the remainder is 0, so 1 is a divisor of 4250)
4250 / 2 = 2125 (the remainder is 0, so 2 is a divisor of 4250)
4250 / 3 = 1416.6666666667 (the remainder is 2, so 3 is not a divisor of 4250)
...
4250 / 4249 = 1.000235349494 (the remainder is 1, so 4249 is not a divisor of 4250)
4250 / 4250 = 1 (the remainder is 0, so 4250 is a divisor of 4250)

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 4250 (i.e. 65.192024052026). 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 $\frac{N}{d} = D$ )

4250 / 1 = 4250 (the remainder is 0, so 1 and 4250 are divisors of 4250)
4250 / 2 = 2125 (the remainder is 0, so 2 and 2125 are divisors of 4250)
4250 / 3 = 1416.6666666667 (the remainder is 2, so 3 is not a divisor of 4250)
...
4250 / 64 = 66.40625 (the remainder is 26, so 64 is not a divisor of 4250)
4250 / 65 = 65.384615384615 (the remainder is 25, so 65 is not a divisor of 4250)