What are the divisors of 1370?

1, 2, 5, 10, 137, 274, 685, 1370

There is a total of 8 positive divisors.
The sum of these divisors is 2484.
The arithmetic mean is 310.5.

4 even divisors

2, 10, 274, 1370

4 odd divisors

1, 5, 137, 685

How to compute the divisors of 1370?

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 1370 by each of the numbers from 1 to 1370 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)

1370 / 1 = 1370 (the remainder is 0, so 1 is a divisor of 1370)
1370 / 2 = 685 (the remainder is 0, so 2 is a divisor of 1370)
1370 / 3 = 456.66666666667 (the remainder is 2, so 3 is not a divisor of 1370)
...
1370 / 1369 = 1.0007304601899 (the remainder is 1, so 1369 is not a divisor of 1370)
1370 / 1370 = 1 (the remainder is 0, so 1370 is a divisor of 1370)

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 1370 (i.e. 37.013511046643). 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 $\frac{N}{d} = D$ )

1370 / 1 = 1370 (the remainder is 0, so 1 and 1370 are divisors of 1370)
1370 / 2 = 685 (the remainder is 0, so 2 and 685 are divisors of 1370)
1370 / 3 = 456.66666666667 (the remainder is 2, so 3 is not a divisor of 1370)
...
1370 / 36 = 38.055555555556 (the remainder is 2, so 36 is not a divisor of 1370)
1370 / 37 = 37.027027027027 (the remainder is 1, so 37 is not a divisor of 1370)