What are the divisors of 1480?

1, 2, 4, 5, 8, 10, 20, 37, 40, 74, 148, 185, 296, 370, 740, 1480

There is a total of 16 positive divisors.
The sum of these divisors is 3420.
The arithmetic mean is 213.75.

12 even divisors

2, 4, 8, 10, 20, 40, 74, 148, 296, 370, 740, 1480

4 odd divisors

1, 5, 37, 185

How to compute the divisors of 1480?

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 1480 by each of the numbers from 1 to 1480 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)

1480 / 1 = 1480 (the remainder is 0, so 1 is a divisor of 1480)
1480 / 2 = 740 (the remainder is 0, so 2 is a divisor of 1480)
1480 / 3 = 493.33333333333 (the remainder is 1, so 3 is not a divisor of 1480)
...
1480 / 1479 = 1.000676132522 (the remainder is 1, so 1479 is not a divisor of 1480)
1480 / 1480 = 1 (the remainder is 0, so 1480 is a divisor of 1480)

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 1480 (i.e. 38.470768123343). 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 $\frac{N}{d} = D$ )

1480 / 1 = 1480 (the remainder is 0, so 1 and 1480 are divisors of 1480)
1480 / 2 = 740 (the remainder is 0, so 2 and 740 are divisors of 1480)
1480 / 3 = 493.33333333333 (the remainder is 1, so 3 is not a divisor of 1480)
...
1480 / 37 = 40 (the remainder is 0, so 37 and 40 are divisors of 1480)
1480 / 38 = 38.947368421053 (the remainder is 36, so 38 is not a divisor of 1480)