What are the divisors of 1498?

1, 2, 7, 14, 107, 214, 749, 1498

There is a total of 8 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 324.

4 even divisors

2, 14, 214, 1498

4 odd divisors

1, 7, 107, 749

How to compute the divisors of 1498?

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 1498 by each of the numbers from 1 to 1498 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)

1498 / 1 = 1498 (the remainder is 0, so 1 is a divisor of 1498)
1498 / 2 = 749 (the remainder is 0, so 2 is a divisor of 1498)
1498 / 3 = 499.33333333333 (the remainder is 1, so 3 is not a divisor of 1498)
...
1498 / 1497 = 1.000668002672 (the remainder is 1, so 1497 is not a divisor of 1498)
1498 / 1498 = 1 (the remainder is 0, so 1498 is a divisor of 1498)

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 1498 (i.e. 38.704004960727). 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 $\frac{N}{d} = D$ )

1498 / 1 = 1498 (the remainder is 0, so 1 and 1498 are divisors of 1498)
1498 / 2 = 749 (the remainder is 0, so 2 and 749 are divisors of 1498)
1498 / 3 = 499.33333333333 (the remainder is 1, so 3 is not a divisor of 1498)
...
1498 / 37 = 40.486486486486 (the remainder is 18, so 37 is not a divisor of 1498)
1498 / 38 = 39.421052631579 (the remainder is 16, so 38 is not a divisor of 1498)