What are the divisors of 610?

1, 2, 5, 10, 61, 122, 305, 610

There is a total of 8 positive divisors.
The sum of these divisors is 1116.
The arithmetic mean is 139.5.

4 even divisors

2, 10, 122, 610

4 odd divisors

1, 5, 61, 305

How to compute the divisors of 610?

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 610 by each of the numbers from 1 to 610 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)

610 / 1 = 610 (the remainder is 0, so 1 is a divisor of 610)
610 / 2 = 305 (the remainder is 0, so 2 is a divisor of 610)
610 / 3 = 203.33333333333 (the remainder is 1, so 3 is not a divisor of 610)
...
610 / 609 = 1.0016420361248 (the remainder is 1, so 609 is not a divisor of 610)
610 / 610 = 1 (the remainder is 0, so 610 is a divisor of 610)

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 610 (i.e. 24.698178070457). 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 $\frac{N}{d} = D$ )

610 / 1 = 610 (the remainder is 0, so 1 and 610 are divisors of 610)
610 / 2 = 305 (the remainder is 0, so 2 and 305 are divisors of 610)
610 / 3 = 203.33333333333 (the remainder is 1, so 3 is not a divisor of 610)
...
610 / 23 = 26.521739130435 (the remainder is 12, so 23 is not a divisor of 610)
610 / 24 = 25.416666666667 (the remainder is 10, so 24 is not a divisor of 610)