What are the divisors of 4921?

1, 7, 19, 37, 133, 259, 703, 4921

There is a total of 8 positive divisors.
The sum of these divisors is 6080.
The arithmetic mean is 760.

8 odd divisors

1, 7, 19, 37, 133, 259, 703, 4921

How to compute the divisors of 4921?

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 4921 by each of the numbers from 1 to 4921 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)

4921 / 1 = 4921 (the remainder is 0, so 1 is a divisor of 4921)
4921 / 2 = 2460.5 (the remainder is 1, so 2 is not a divisor of 4921)
4921 / 3 = 1640.3333333333 (the remainder is 1, so 3 is not a divisor of 4921)
...
4921 / 4920 = 1.0002032520325 (the remainder is 1, so 4920 is not a divisor of 4921)
4921 / 4921 = 1 (the remainder is 0, so 4921 is a divisor of 4921)

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 4921 (i.e. 70.149839629182). 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 $\frac{N}{d} = D$ )

4921 / 1 = 4921 (the remainder is 0, so 1 and 4921 are divisors of 4921)
4921 / 2 = 2460.5 (the remainder is 1, so 2 is not a divisor of 4921)
4921 / 3 = 1640.3333333333 (the remainder is 1, so 3 is not a divisor of 4921)
...
4921 / 69 = 71.31884057971 (the remainder is 22, so 69 is not a divisor of 4921)
4921 / 70 = 70.3 (the remainder is 21, so 70 is not a divisor of 4921)