What are the divisors of 616?

1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616

There is a total of 16 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 90.

12 even divisors

2, 4, 8, 14, 22, 28, 44, 56, 88, 154, 308, 616

4 odd divisors

1, 7, 11, 77

How to compute the divisors of 616?

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 616 by each of the numbers from 1 to 616 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)

616 / 1 = 616 (the remainder is 0, so 1 is a divisor of 616)
616 / 2 = 308 (the remainder is 0, so 2 is a divisor of 616)
616 / 3 = 205.33333333333 (the remainder is 1, so 3 is not a divisor of 616)
...
616 / 615 = 1.0016260162602 (the remainder is 1, so 615 is not a divisor of 616)
616 / 616 = 1 (the remainder is 0, so 616 is a divisor of 616)

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 616 (i.e. 24.819347291982). 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 $\frac{N}{d} = D$ )

616 / 1 = 616 (the remainder is 0, so 1 and 616 are divisors of 616)
616 / 2 = 308 (the remainder is 0, so 2 and 308 are divisors of 616)
616 / 3 = 205.33333333333 (the remainder is 1, so 3 is not a divisor of 616)
...
616 / 23 = 26.782608695652 (the remainder is 18, so 23 is not a divisor of 616)
616 / 24 = 25.666666666667 (the remainder is 16, so 24 is not a divisor of 616)