What are the divisors of 4952?

1, 2, 4, 8, 619, 1238, 2476, 4952

There is a total of 8 positive divisors.
The sum of these divisors is 9300.
The arithmetic mean is 1162.5.

6 even divisors

2, 4, 8, 1238, 2476, 4952

2 odd divisors

1, 619

How to compute the divisors of 4952?

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 4952 by each of the numbers from 1 to 4952 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)

4952 / 1 = 4952 (the remainder is 0, so 1 is a divisor of 4952)
4952 / 2 = 2476 (the remainder is 0, so 2 is a divisor of 4952)
4952 / 3 = 1650.6666666667 (the remainder is 2, so 3 is not a divisor of 4952)
...
4952 / 4951 = 1.0002019793981 (the remainder is 1, so 4951 is not a divisor of 4952)
4952 / 4952 = 1 (the remainder is 0, so 4952 is a divisor of 4952)

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 4952 (i.e. 70.370448343037). 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 $\frac{N}{d} = D$ )

4952 / 1 = 4952 (the remainder is 0, so 1 and 4952 are divisors of 4952)
4952 / 2 = 2476 (the remainder is 0, so 2 and 2476 are divisors of 4952)
4952 / 3 = 1650.6666666667 (the remainder is 2, so 3 is not a divisor of 4952)
...
4952 / 69 = 71.768115942029 (the remainder is 53, so 69 is not a divisor of 4952)
4952 / 70 = 70.742857142857 (the remainder is 52, so 70 is not a divisor of 4952)