What are the divisors of 4970?

1, 2, 5, 7, 10, 14, 35, 70, 71, 142, 355, 497, 710, 994, 2485, 4970

There is a total of 16 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 648.

8 even divisors

2, 10, 14, 70, 142, 710, 994, 4970

8 odd divisors

1, 5, 7, 35, 71, 355, 497, 2485

How to compute the divisors of 4970?

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 4970 by each of the numbers from 1 to 4970 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)

4970 / 1 = 4970 (the remainder is 0, so 1 is a divisor of 4970)
4970 / 2 = 2485 (the remainder is 0, so 2 is a divisor of 4970)
4970 / 3 = 1656.6666666667 (the remainder is 2, so 3 is not a divisor of 4970)
...
4970 / 4969 = 1.000201247736 (the remainder is 1, so 4969 is not a divisor of 4970)
4970 / 4970 = 1 (the remainder is 0, so 4970 is a divisor of 4970)

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 4970 (i.e. 70.498226928058). 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 $\frac{N}{d} = D$ )

4970 / 1 = 4970 (the remainder is 0, so 1 and 4970 are divisors of 4970)
4970 / 2 = 2485 (the remainder is 0, so 2 and 2485 are divisors of 4970)
4970 / 3 = 1656.6666666667 (the remainder is 2, so 3 is not a divisor of 4970)
...
4970 / 69 = 72.028985507246 (the remainder is 2, so 69 is not a divisor of 4970)
4970 / 70 = 71 (the remainder is 0, so 70 and 71 are divisors of 4970)