What are the divisors of 1270?

1, 2, 5, 10, 127, 254, 635, 1270

There is a total of 8 positive divisors.
The sum of these divisors is 2304.
The arithmetic mean is 288.

4 even divisors

2, 10, 254, 1270

4 odd divisors

1, 5, 127, 635

How to compute the divisors of 1270?

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 1270 by each of the numbers from 1 to 1270 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)

1270 / 1 = 1270 (the remainder is 0, so 1 is a divisor of 1270)
1270 / 2 = 635 (the remainder is 0, so 2 is a divisor of 1270)
1270 / 3 = 423.33333333333 (the remainder is 1, so 3 is not a divisor of 1270)
...
1270 / 1269 = 1.0007880220646 (the remainder is 1, so 1269 is not a divisor of 1270)
1270 / 1270 = 1 (the remainder is 0, so 1270 is a divisor of 1270)

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 1270 (i.e. 35.637059362411). 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 $\frac{N}{d} = D$ )

1270 / 1 = 1270 (the remainder is 0, so 1 and 1270 are divisors of 1270)
1270 / 2 = 635 (the remainder is 0, so 2 and 635 are divisors of 1270)
1270 / 3 = 423.33333333333 (the remainder is 1, so 3 is not a divisor of 1270)
...
1270 / 34 = 37.352941176471 (the remainder is 12, so 34 is not a divisor of 1270)
1270 / 35 = 36.285714285714 (the remainder is 10, so 35 is not a divisor of 1270)