What are the divisors of 1570?

1, 2, 5, 10, 157, 314, 785, 1570

There is a total of 8 positive divisors.
The sum of these divisors is 2844.
The arithmetic mean is 355.5.

4 even divisors

2, 10, 314, 1570

4 odd divisors

1, 5, 157, 785

How to compute the divisors of 1570?

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 1570 by each of the numbers from 1 to 1570 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)

1570 / 1 = 1570 (the remainder is 0, so 1 is a divisor of 1570)
1570 / 2 = 785 (the remainder is 0, so 2 is a divisor of 1570)
1570 / 3 = 523.33333333333 (the remainder is 1, so 3 is not a divisor of 1570)
...
1570 / 1569 = 1.0006373486297 (the remainder is 1, so 1569 is not a divisor of 1570)
1570 / 1570 = 1 (the remainder is 0, so 1570 is a divisor of 1570)

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 1570 (i.e. 39.623225512318). 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 $\frac{N}{d} = D$ )

1570 / 1 = 1570 (the remainder is 0, so 1 and 1570 are divisors of 1570)
1570 / 2 = 785 (the remainder is 0, so 2 and 785 are divisors of 1570)
1570 / 3 = 523.33333333333 (the remainder is 1, so 3 is not a divisor of 1570)
...
1570 / 38 = 41.315789473684 (the remainder is 12, so 38 is not a divisor of 1570)
1570 / 39 = 40.25641025641 (the remainder is 10, so 39 is not a divisor of 1570)