What are the divisors of 1478?

1, 2, 739, 1478

There is a total of 4 positive divisors.
The sum of these divisors is 2220.
The arithmetic mean is 555.

2 even divisors

2, 1478

2 odd divisors

1, 739

How to compute the divisors of 1478?

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 1478 by each of the numbers from 1 to 1478 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)

1478 / 1 = 1478 (the remainder is 0, so 1 is a divisor of 1478)
1478 / 2 = 739 (the remainder is 0, so 2 is a divisor of 1478)
1478 / 3 = 492.66666666667 (the remainder is 2, so 3 is not a divisor of 1478)
...
1478 / 1477 = 1.0006770480704 (the remainder is 1, so 1477 is not a divisor of 1478)
1478 / 1478 = 1 (the remainder is 0, so 1478 is a divisor of 1478)

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 1478 (i.e. 38.444765573482). 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 $\frac{N}{d} = D$ )

1478 / 1 = 1478 (the remainder is 0, so 1 and 1478 are divisors of 1478)
1478 / 2 = 739 (the remainder is 0, so 2 and 739 are divisors of 1478)
1478 / 3 = 492.66666666667 (the remainder is 2, so 3 is not a divisor of 1478)
...
1478 / 37 = 39.945945945946 (the remainder is 35, so 37 is not a divisor of 1478)
1478 / 38 = 38.894736842105 (the remainder is 34, so 38 is not a divisor of 1478)