What are the divisors of 1373?

1, 1373

There is a total of 2 positive divisors.
The sum of these divisors is 1374.
The arithmetic mean is 687.

2 odd divisors

1, 1373

How to compute the divisors of 1373?

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 1373 by each of the numbers from 1 to 1373 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)

1373 / 1 = 1373 (the remainder is 0, so 1 is a divisor of 1373)
1373 / 2 = 686.5 (the remainder is 1, so 2 is not a divisor of 1373)
1373 / 3 = 457.66666666667 (the remainder is 2, so 3 is not a divisor of 1373)
...
1373 / 1372 = 1.0007288629738 (the remainder is 1, so 1372 is not a divisor of 1373)
1373 / 1373 = 1 (the remainder is 0, so 1373 is a divisor of 1373)

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 1373 (i.e. 37.054014627298). 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 $\frac{N}{d} = D$ )

1373 / 1 = 1373 (the remainder is 0, so 1 and 1373 are divisors of 1373)
1373 / 2 = 686.5 (the remainder is 1, so 2 is not a divisor of 1373)
1373 / 3 = 457.66666666667 (the remainder is 2, so 3 is not a divisor of 1373)
...
1373 / 36 = 38.138888888889 (the remainder is 5, so 36 is not a divisor of 1373)
1373 / 37 = 37.108108108108 (the remainder is 4, so 37 is not a divisor of 1373)