What are the divisors of 1228?

1, 2, 4, 307, 614, 1228

There is a total of 6 positive divisors.
The sum of these divisors is 2156.
The arithmetic mean is 359.33333333333.

4 even divisors

2, 4, 614, 1228

2 odd divisors

1, 307

How to compute the divisors of 1228?

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 1228 by each of the numbers from 1 to 1228 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)

1228 / 1 = 1228 (the remainder is 0, so 1 is a divisor of 1228)
1228 / 2 = 614 (the remainder is 0, so 2 is a divisor of 1228)
1228 / 3 = 409.33333333333 (the remainder is 1, so 3 is not a divisor of 1228)
...
1228 / 1227 = 1.000814995925 (the remainder is 1, so 1227 is not a divisor of 1228)
1228 / 1228 = 1 (the remainder is 0, so 1228 is a divisor of 1228)

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 1228 (i.e. 35.04283093587). 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 $\frac{N}{d} = D$ )

1228 / 1 = 1228 (the remainder is 0, so 1 and 1228 are divisors of 1228)
1228 / 2 = 614 (the remainder is 0, so 2 and 614 are divisors of 1228)
1228 / 3 = 409.33333333333 (the remainder is 1, so 3 is not a divisor of 1228)
...
1228 / 34 = 36.117647058824 (the remainder is 4, so 34 is not a divisor of 1228)
1228 / 35 = 35.085714285714 (the remainder is 3, so 35 is not a divisor of 1228)