What are the divisors of 1492?

1, 2, 4, 373, 746, 1492

There is a total of 6 positive divisors.
The sum of these divisors is 2618.
The arithmetic mean is 436.33333333333.

4 even divisors

2, 4, 746, 1492

2 odd divisors

1, 373

How to compute the divisors of 1492?

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 1492 by each of the numbers from 1 to 1492 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)

1492 / 1 = 1492 (the remainder is 0, so 1 is a divisor of 1492)
1492 / 2 = 746 (the remainder is 0, so 2 is a divisor of 1492)
1492 / 3 = 497.33333333333 (the remainder is 1, so 3 is not a divisor of 1492)
...
1492 / 1491 = 1.0006706908115 (the remainder is 1, so 1491 is not a divisor of 1492)
1492 / 1492 = 1 (the remainder is 0, so 1492 is a divisor of 1492)

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 1492 (i.e. 38.626415831656). 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 $\frac{N}{d} = D$ )

1492 / 1 = 1492 (the remainder is 0, so 1 and 1492 are divisors of 1492)
1492 / 2 = 746 (the remainder is 0, so 2 and 746 are divisors of 1492)
1492 / 3 = 497.33333333333 (the remainder is 1, so 3 is not a divisor of 1492)
...
1492 / 37 = 40.324324324324 (the remainder is 12, so 37 is not a divisor of 1492)
1492 / 38 = 39.263157894737 (the remainder is 10, so 38 is not a divisor of 1492)