What are the divisors of 1372?

1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372

There is a total of 12 positive divisors.
The sum of these divisors is 2800.
The arithmetic mean is 233.33333333333.

8 even divisors

2, 4, 14, 28, 98, 196, 686, 1372

4 odd divisors

1, 7, 49, 343

How to compute the divisors of 1372?

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 1372 by each of the numbers from 1 to 1372 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)

1372 / 1 = 1372 (the remainder is 0, so 1 is a divisor of 1372)
1372 / 2 = 686 (the remainder is 0, so 2 is a divisor of 1372)
1372 / 3 = 457.33333333333 (the remainder is 1, so 3 is not a divisor of 1372)
...
1372 / 1371 = 1.0007293946025 (the remainder is 1, so 1371 is not a divisor of 1372)
1372 / 1372 = 1 (the remainder is 0, so 1372 is a divisor of 1372)

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 1372 (i.e. 37.040518354904). 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 $\frac{N}{d} = D$ )

1372 / 1 = 1372 (the remainder is 0, so 1 and 1372 are divisors of 1372)
1372 / 2 = 686 (the remainder is 0, so 2 and 686 are divisors of 1372)
1372 / 3 = 457.33333333333 (the remainder is 1, so 3 is not a divisor of 1372)
...
1372 / 36 = 38.111111111111 (the remainder is 4, so 36 is not a divisor of 1372)
1372 / 37 = 37.081081081081 (the remainder is 3, so 37 is not a divisor of 1372)