What are the divisors of 4948?

1, 2, 4, 1237, 2474, 4948

There is a total of 6 positive divisors.
The sum of these divisors is 8666.
The arithmetic mean is 1444.3333333333.

4 even divisors

2, 4, 2474, 4948

2 odd divisors

1, 1237

How to compute the divisors of 4948?

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 4948 by each of the numbers from 1 to 4948 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)

4948 / 1 = 4948 (the remainder is 0, so 1 is a divisor of 4948)
4948 / 2 = 2474 (the remainder is 0, so 2 is a divisor of 4948)
4948 / 3 = 1649.3333333333 (the remainder is 1, so 3 is not a divisor of 4948)
...
4948 / 4947 = 1.0002021427128 (the remainder is 1, so 4947 is not a divisor of 4948)
4948 / 4948 = 1 (the remainder is 0, so 4948 is a divisor of 4948)

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 4948 (i.e. 70.342021580276). 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 $\frac{N}{d} = D$ )

4948 / 1 = 4948 (the remainder is 0, so 1 and 4948 are divisors of 4948)
4948 / 2 = 2474 (the remainder is 0, so 2 and 2474 are divisors of 4948)
4948 / 3 = 1649.3333333333 (the remainder is 1, so 3 is not a divisor of 4948)
...
4948 / 69 = 71.710144927536 (the remainder is 49, so 69 is not a divisor of 4948)
4948 / 70 = 70.685714285714 (the remainder is 48, so 70 is not a divisor of 4948)