What are the divisors of 4154?

1, 2, 31, 62, 67, 134, 2077, 4154

There is a total of 8 positive divisors.
The sum of these divisors is 6528.
The arithmetic mean is 816.

4 even divisors

2, 62, 134, 4154

4 odd divisors

1, 31, 67, 2077

How to compute the divisors of 4154?

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 4154 by each of the numbers from 1 to 4154 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)

4154 / 1 = 4154 (the remainder is 0, so 1 is a divisor of 4154)
4154 / 2 = 2077 (the remainder is 0, so 2 is a divisor of 4154)
4154 / 3 = 1384.6666666667 (the remainder is 2, so 3 is not a divisor of 4154)
...
4154 / 4153 = 1.0002407897905 (the remainder is 1, so 4153 is not a divisor of 4154)
4154 / 4154 = 1 (the remainder is 0, so 4154 is a divisor of 4154)

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 4154 (i.e. 64.451532177288). 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 $\frac{N}{d} = D$ )

4154 / 1 = 4154 (the remainder is 0, so 1 and 4154 are divisors of 4154)
4154 / 2 = 2077 (the remainder is 0, so 2 and 2077 are divisors of 4154)
4154 / 3 = 1384.6666666667 (the remainder is 2, so 3 is not a divisor of 4154)
...
4154 / 63 = 65.936507936508 (the remainder is 59, so 63 is not a divisor of 4154)
4154 / 64 = 64.90625 (the remainder is 58, so 64 is not a divisor of 4154)