What are the divisors of 1176?

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 49, 56, 84, 98, 147, 168, 196, 294, 392, 588, 1176

There is a total of 24 positive divisors.
The sum of these divisors is 3420.
The arithmetic mean is 142.5.

18 even divisors

2, 4, 6, 8, 12, 14, 24, 28, 42, 56, 84, 98, 168, 196, 294, 392, 588, 1176

6 odd divisors

1, 3, 7, 21, 49, 147

How to compute the divisors of 1176?

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 1176 by each of the numbers from 1 to 1176 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)

1176 / 1 = 1176 (the remainder is 0, so 1 is a divisor of 1176)
1176 / 2 = 588 (the remainder is 0, so 2 is a divisor of 1176)
1176 / 3 = 392 (the remainder is 0, so 3 is a divisor of 1176)
...
1176 / 1175 = 1.0008510638298 (the remainder is 1, so 1175 is not a divisor of 1176)
1176 / 1176 = 1 (the remainder is 0, so 1176 is a divisor of 1176)

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 1176 (i.e. 34.292856398964). 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 $\frac{N}{d} = D$ )

1176 / 1 = 1176 (the remainder is 0, so 1 and 1176 are divisors of 1176)
1176 / 2 = 588 (the remainder is 0, so 2 and 588 are divisors of 1176)
1176 / 3 = 392 (the remainder is 0, so 3 and 392 are divisors of 1176)
...
1176 / 33 = 35.636363636364 (the remainder is 21, so 33 is not a divisor of 1176)
1176 / 34 = 34.588235294118 (the remainder is 20, so 34 is not a divisor of 1176)