What are the divisors of 1340?

1, 2, 4, 5, 10, 20, 67, 134, 268, 335, 670, 1340

There is a total of 12 positive divisors.
The sum of these divisors is 2856.
The arithmetic mean is 238.

8 even divisors

2, 4, 10, 20, 134, 268, 670, 1340

4 odd divisors

1, 5, 67, 335

How to compute the divisors of 1340?

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 1340 by each of the numbers from 1 to 1340 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)

1340 / 1 = 1340 (the remainder is 0, so 1 is a divisor of 1340)
1340 / 2 = 670 (the remainder is 0, so 2 is a divisor of 1340)
1340 / 3 = 446.66666666667 (the remainder is 2, so 3 is not a divisor of 1340)
...
1340 / 1339 = 1.0007468259895 (the remainder is 1, so 1339 is not a divisor of 1340)
1340 / 1340 = 1 (the remainder is 0, so 1340 is a divisor of 1340)

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 1340 (i.e. 36.606010435446). 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 $\frac{N}{d} = D$ )

1340 / 1 = 1340 (the remainder is 0, so 1 and 1340 are divisors of 1340)
1340 / 2 = 670 (the remainder is 0, so 2 and 670 are divisors of 1340)
1340 / 3 = 446.66666666667 (the remainder is 2, so 3 is not a divisor of 1340)
...
1340 / 35 = 38.285714285714 (the remainder is 10, so 35 is not a divisor of 1340)
1340 / 36 = 37.222222222222 (the remainder is 8, so 36 is not a divisor of 1340)