What are the divisors of 1348?

1, 2, 4, 337, 674, 1348

There is a total of 6 positive divisors.
The sum of these divisors is 2366.
The arithmetic mean is 394.33333333333.

4 even divisors

2, 4, 674, 1348

2 odd divisors

1, 337

How to compute the divisors of 1348?

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 1348 by each of the numbers from 1 to 1348 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)

1348 / 1 = 1348 (the remainder is 0, so 1 is a divisor of 1348)
1348 / 2 = 674 (the remainder is 0, so 2 is a divisor of 1348)
1348 / 3 = 449.33333333333 (the remainder is 1, so 3 is not a divisor of 1348)
...
1348 / 1347 = 1.0007423904974 (the remainder is 1, so 1347 is not a divisor of 1348)
1348 / 1348 = 1 (the remainder is 0, so 1348 is a divisor of 1348)

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 1348 (i.e. 36.715119501372). 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 $\frac{N}{d} = D$ )

1348 / 1 = 1348 (the remainder is 0, so 1 and 1348 are divisors of 1348)
1348 / 2 = 674 (the remainder is 0, so 2 and 674 are divisors of 1348)
1348 / 3 = 449.33333333333 (the remainder is 1, so 3 is not a divisor of 1348)
...
1348 / 35 = 38.514285714286 (the remainder is 18, so 35 is not a divisor of 1348)
1348 / 36 = 37.444444444444 (the remainder is 16, so 36 is not a divisor of 1348)