What are the divisors of 4272?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 89, 178, 267, 356, 534, 712, 1068, 1424, 2136, 4272

There is a total of 20 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 558.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 178, 356, 534, 712, 1068, 1424, 2136, 4272

4 odd divisors

1, 3, 89, 267

How to compute the divisors of 4272?

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 4272 by each of the numbers from 1 to 4272 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)

4272 / 1 = 4272 (the remainder is 0, so 1 is a divisor of 4272)
4272 / 2 = 2136 (the remainder is 0, so 2 is a divisor of 4272)
4272 / 3 = 1424 (the remainder is 0, so 3 is a divisor of 4272)
...
4272 / 4271 = 1.0002341372044 (the remainder is 1, so 4271 is not a divisor of 4272)
4272 / 4272 = 1 (the remainder is 0, so 4272 is a divisor of 4272)

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 4272 (i.e. 65.360538553473). 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 $\frac{N}{d} = D$ )

4272 / 1 = 4272 (the remainder is 0, so 1 and 4272 are divisors of 4272)
4272 / 2 = 2136 (the remainder is 0, so 2 and 2136 are divisors of 4272)
4272 / 3 = 1424 (the remainder is 0, so 3 and 1424 are divisors of 4272)
...
4272 / 64 = 66.75 (the remainder is 48, so 64 is not a divisor of 4272)
4272 / 65 = 65.723076923077 (the remainder is 47, so 65 is not a divisor of 4272)