What are the divisors of 1552?

1, 2, 4, 8, 16, 97, 194, 388, 776, 1552

There is a total of 10 positive divisors.
The sum of these divisors is 3038.
The arithmetic mean is 303.8.

8 even divisors

2, 4, 8, 16, 194, 388, 776, 1552

2 odd divisors

1, 97

How to compute the divisors of 1552?

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 1552 by each of the numbers from 1 to 1552 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)

1552 / 1 = 1552 (the remainder is 0, so 1 is a divisor of 1552)
1552 / 2 = 776 (the remainder is 0, so 2 is a divisor of 1552)
1552 / 3 = 517.33333333333 (the remainder is 1, so 3 is not a divisor of 1552)
...
1552 / 1551 = 1.0006447453256 (the remainder is 1, so 1551 is not a divisor of 1552)
1552 / 1552 = 1 (the remainder is 0, so 1552 is a divisor of 1552)

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 1552 (i.e. 39.395431207184). 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 $\frac{N}{d} = D$ )

1552 / 1 = 1552 (the remainder is 0, so 1 and 1552 are divisors of 1552)
1552 / 2 = 776 (the remainder is 0, so 2 and 776 are divisors of 1552)
1552 / 3 = 517.33333333333 (the remainder is 1, so 3 is not a divisor of 1552)
...
1552 / 38 = 40.842105263158 (the remainder is 32, so 38 is not a divisor of 1552)
1552 / 39 = 39.794871794872 (the remainder is 31, so 39 is not a divisor of 1552)