What are the divisors of 1470?

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 49, 70, 98, 105, 147, 210, 245, 294, 490, 735, 1470

There is a total of 24 positive divisors.
The sum of these divisors is 4104.
The arithmetic mean is 171.

12 even divisors

2, 6, 10, 14, 30, 42, 70, 98, 210, 294, 490, 1470

12 odd divisors

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735

How to compute the divisors of 1470?

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 1470 by each of the numbers from 1 to 1470 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)

1470 / 1 = 1470 (the remainder is 0, so 1 is a divisor of 1470)
1470 / 2 = 735 (the remainder is 0, so 2 is a divisor of 1470)
1470 / 3 = 490 (the remainder is 0, so 3 is a divisor of 1470)
...
1470 / 1469 = 1.000680735194 (the remainder is 1, so 1469 is not a divisor of 1470)
1470 / 1470 = 1 (the remainder is 0, so 1470 is a divisor of 1470)

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 1470 (i.e. 38.340579025362). 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 $\frac{N}{d} = D$ )

1470 / 1 = 1470 (the remainder is 0, so 1 and 1470 are divisors of 1470)
1470 / 2 = 735 (the remainder is 0, so 2 and 735 are divisors of 1470)
1470 / 3 = 490 (the remainder is 0, so 3 and 490 are divisors of 1470)
...
1470 / 37 = 39.72972972973 (the remainder is 27, so 37 is not a divisor of 1470)
1470 / 38 = 38.684210526316 (the remainder is 26, so 38 is not a divisor of 1470)