What are the divisors of 1448?

1, 2, 4, 8, 181, 362, 724, 1448

There is a total of 8 positive divisors.
The sum of these divisors is 2730.
The arithmetic mean is 341.25.

6 even divisors

2, 4, 8, 362, 724, 1448

2 odd divisors

1, 181

How to compute the divisors of 1448?

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 1448 by each of the numbers from 1 to 1448 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)

1448 / 1 = 1448 (the remainder is 0, so 1 is a divisor of 1448)
1448 / 2 = 724 (the remainder is 0, so 2 is a divisor of 1448)
1448 / 3 = 482.66666666667 (the remainder is 2, so 3 is not a divisor of 1448)
...
1448 / 1447 = 1.0006910850035 (the remainder is 1, so 1447 is not a divisor of 1448)
1448 / 1448 = 1 (the remainder is 0, so 1448 is a divisor of 1448)

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 1448 (i.e. 38.052595180881). 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 $\frac{N}{d} = D$ )

1448 / 1 = 1448 (the remainder is 0, so 1 and 1448 are divisors of 1448)
1448 / 2 = 724 (the remainder is 0, so 2 and 724 are divisors of 1448)
1448 / 3 = 482.66666666667 (the remainder is 2, so 3 is not a divisor of 1448)
...
1448 / 37 = 39.135135135135 (the remainder is 5, so 37 is not a divisor of 1448)
1448 / 38 = 38.105263157895 (the remainder is 4, so 38 is not a divisor of 1448)