What are the divisors of 1474?

1, 2, 11, 22, 67, 134, 737, 1474

There is a total of 8 positive divisors.
The sum of these divisors is 2448.
The arithmetic mean is 306.

4 even divisors

2, 22, 134, 1474

4 odd divisors

1, 11, 67, 737

How to compute the divisors of 1474?

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 1474 by each of the numbers from 1 to 1474 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)

1474 / 1 = 1474 (the remainder is 0, so 1 is a divisor of 1474)
1474 / 2 = 737 (the remainder is 0, so 2 is a divisor of 1474)
1474 / 3 = 491.33333333333 (the remainder is 1, so 3 is not a divisor of 1474)
...
1474 / 1473 = 1.0006788866259 (the remainder is 1, so 1473 is not a divisor of 1474)
1474 / 1474 = 1 (the remainder is 0, so 1474 is a divisor of 1474)

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 1474 (i.e. 38.392707640905). 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 $\frac{N}{d} = D$ )

1474 / 1 = 1474 (the remainder is 0, so 1 and 1474 are divisors of 1474)
1474 / 2 = 737 (the remainder is 0, so 2 and 737 are divisors of 1474)
1474 / 3 = 491.33333333333 (the remainder is 1, so 3 is not a divisor of 1474)
...
1474 / 37 = 39.837837837838 (the remainder is 31, so 37 is not a divisor of 1474)
1474 / 38 = 38.789473684211 (the remainder is 30, so 38 is not a divisor of 1474)