What are the divisors of 1472?

1, 2, 4, 8, 16, 23, 32, 46, 64, 92, 184, 368, 736, 1472

There is a total of 14 positive divisors.
The sum of these divisors is 3048.
The arithmetic mean is 217.71428571429.

12 even divisors

2, 4, 8, 16, 32, 46, 64, 92, 184, 368, 736, 1472

2 odd divisors

1, 23

How to compute the divisors of 1472?

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 1472 by each of the numbers from 1 to 1472 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)

1472 / 1 = 1472 (the remainder is 0, so 1 is a divisor of 1472)
1472 / 2 = 736 (the remainder is 0, so 2 is a divisor of 1472)
1472 / 3 = 490.66666666667 (the remainder is 2, so 3 is not a divisor of 1472)
...
1472 / 1471 = 1.0006798096533 (the remainder is 1, so 1471 is not a divisor of 1472)
1472 / 1472 = 1 (the remainder is 0, so 1472 is a divisor of 1472)

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 1472 (i.e. 38.366652186502). 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 $\frac{N}{d} = D$ )

1472 / 1 = 1472 (the remainder is 0, so 1 and 1472 are divisors of 1472)
1472 / 2 = 736 (the remainder is 0, so 2 and 736 are divisors of 1472)
1472 / 3 = 490.66666666667 (the remainder is 2, so 3 is not a divisor of 1472)
...
1472 / 37 = 39.783783783784 (the remainder is 29, so 37 is not a divisor of 1472)
1472 / 38 = 38.736842105263 (the remainder is 28, so 38 is not a divisor of 1472)