What are the divisors of 1424?

1, 2, 4, 8, 16, 89, 178, 356, 712, 1424

There is a total of 10 positive divisors.
The sum of these divisors is 2790.
The arithmetic mean is 279.

8 even divisors

2, 4, 8, 16, 178, 356, 712, 1424

2 odd divisors

1, 89

How to compute the divisors of 1424?

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 1424 by each of the numbers from 1 to 1424 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)

1424 / 1 = 1424 (the remainder is 0, so 1 is a divisor of 1424)
1424 / 2 = 712 (the remainder is 0, so 2 is a divisor of 1424)
1424 / 3 = 474.66666666667 (the remainder is 2, so 3 is not a divisor of 1424)
...
1424 / 1423 = 1.0007027406887 (the remainder is 1, so 1423 is not a divisor of 1424)
1424 / 1424 = 1 (the remainder is 0, so 1424 is a divisor of 1424)

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 1424 (i.e. 37.735924528226). 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 $\frac{N}{d} = D$ )

1424 / 1 = 1424 (the remainder is 0, so 1 and 1424 are divisors of 1424)
1424 / 2 = 712 (the remainder is 0, so 2 and 712 are divisors of 1424)
1424 / 3 = 474.66666666667 (the remainder is 2, so 3 is not a divisor of 1424)
...
1424 / 36 = 39.555555555556 (the remainder is 20, so 36 is not a divisor of 1424)
1424 / 37 = 38.486486486486 (the remainder is 18, so 37 is not a divisor of 1424)