What are the divisors of 1553?

1, 1553

There is a total of 2 positive divisors.
The sum of these divisors is 1554.
The arithmetic mean is 777.

2 odd divisors

1, 1553

How to compute the divisors of 1553?

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 1553 by each of the numbers from 1 to 1553 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)

1553 / 1 = 1553 (the remainder is 0, so 1 is a divisor of 1553)
1553 / 2 = 776.5 (the remainder is 1, so 2 is not a divisor of 1553)
1553 / 3 = 517.66666666667 (the remainder is 2, so 3 is not a divisor of 1553)
...
1553 / 1552 = 1.0006443298969 (the remainder is 1, so 1552 is not a divisor of 1553)
1553 / 1553 = 1 (the remainder is 0, so 1553 is a divisor of 1553)

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 1553 (i.e. 39.408120990476). 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 $\frac{N}{d} = D$ )

1553 / 1 = 1553 (the remainder is 0, so 1 and 1553 are divisors of 1553)
1553 / 2 = 776.5 (the remainder is 1, so 2 is not a divisor of 1553)
1553 / 3 = 517.66666666667 (the remainder is 2, so 3 is not a divisor of 1553)
...
1553 / 38 = 40.868421052632 (the remainder is 33, so 38 is not a divisor of 1553)
1553 / 39 = 39.820512820513 (the remainder is 32, so 39 is not a divisor of 1553)