What are the divisors of 2932?

1, 2, 4, 733, 1466, 2932

There is a total of 6 positive divisors.
The sum of these divisors is 5138.
The arithmetic mean is 856.33333333333.

4 even divisors

2, 4, 1466, 2932

2 odd divisors

1, 733

How to compute the divisors of 2932?

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 2932 by each of the numbers from 1 to 2932 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)

2932 / 1 = 2932 (the remainder is 0, so 1 is a divisor of 2932)
2932 / 2 = 1466 (the remainder is 0, so 2 is a divisor of 2932)
2932 / 3 = 977.33333333333 (the remainder is 1, so 3 is not a divisor of 2932)
...
2932 / 2931 = 1.0003411804845 (the remainder is 1, so 2931 is not a divisor of 2932)
2932 / 2932 = 1 (the remainder is 0, so 2932 is a divisor of 2932)

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 2932 (i.e. 54.147945482724). 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 $\frac{N}{d} = D$ )

2932 / 1 = 2932 (the remainder is 0, so 1 and 2932 are divisors of 2932)
2932 / 2 = 1466 (the remainder is 0, so 2 and 1466 are divisors of 2932)
2932 / 3 = 977.33333333333 (the remainder is 1, so 3 is not a divisor of 2932)
...
2932 / 53 = 55.320754716981 (the remainder is 17, so 53 is not a divisor of 2932)
2932 / 54 = 54.296296296296 (the remainder is 16, so 54 is not a divisor of 2932)