What are the divisors of 4900?

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 49, 50, 70, 98, 100, 140, 175, 196, 245, 350, 490, 700, 980, 1225, 2450, 4900

There is a total of 27 positive divisors.
The sum of these divisors is 12369.
The arithmetic mean is 458.11111111111.

18 even divisors

2, 4, 10, 14, 20, 28, 50, 70, 98, 100, 140, 196, 350, 490, 700, 980, 2450, 4900

9 odd divisors

1, 5, 7, 25, 35, 49, 175, 245, 1225

How to compute the divisors of 4900?

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 4900 by each of the numbers from 1 to 4900 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)

4900 / 1 = 4900 (the remainder is 0, so 1 is a divisor of 4900)
4900 / 2 = 2450 (the remainder is 0, so 2 is a divisor of 4900)
4900 / 3 = 1633.3333333333 (the remainder is 1, so 3 is not a divisor of 4900)
...
4900 / 4899 = 1.0002041232905 (the remainder is 1, so 4899 is not a divisor of 4900)
4900 / 4900 = 1 (the remainder is 0, so 4900 is a divisor of 4900)

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 4900 (i.e. 70). 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 $\frac{N}{d} = D$ )

4900 / 1 = 4900 (the remainder is 0, so 1 and 4900 are divisors of 4900)
4900 / 2 = 2450 (the remainder is 0, so 2 and 2450 are divisors of 4900)
4900 / 3 = 1633.3333333333 (the remainder is 1, so 3 is not a divisor of 4900)
...
4900 / 69 = 71.014492753623 (the remainder is 1, so 69 is not a divisor of 4900)
4900 / 70 = 70 (the remainder is 0, so 70 and 70 are divisors of 4900)