What are the divisors of 1172?

1, 2, 4, 293, 586, 1172

There is a total of 6 positive divisors.
The sum of these divisors is 2058.
The arithmetic mean is 343.

4 even divisors

2, 4, 586, 1172

2 odd divisors

1, 293

How to compute the divisors of 1172?

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 1172 by each of the numbers from 1 to 1172 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)

1172 / 1 = 1172 (the remainder is 0, so 1 is a divisor of 1172)
1172 / 2 = 586 (the remainder is 0, so 2 is a divisor of 1172)
1172 / 3 = 390.66666666667 (the remainder is 2, so 3 is not a divisor of 1172)
...
1172 / 1171 = 1.000853970965 (the remainder is 1, so 1171 is not a divisor of 1172)
1172 / 1172 = 1 (the remainder is 0, so 1172 is a divisor of 1172)

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 1172 (i.e. 34.234485537247). 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 $\frac{N}{d} = D$ )

1172 / 1 = 1172 (the remainder is 0, so 1 and 1172 are divisors of 1172)
1172 / 2 = 586 (the remainder is 0, so 2 and 586 are divisors of 1172)
1172 / 3 = 390.66666666667 (the remainder is 2, so 3 is not a divisor of 1172)
...
1172 / 33 = 35.515151515152 (the remainder is 17, so 33 is not a divisor of 1172)
1172 / 34 = 34.470588235294 (the remainder is 16, so 34 is not a divisor of 1172)