What are the divisors of 4951?

1, 4951

There is a total of 2 positive divisors.
The sum of these divisors is 4952.
The arithmetic mean is 2476.

2 odd divisors

1, 4951

How to compute the divisors of 4951?

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 4951 by each of the numbers from 1 to 4951 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)

4951 / 1 = 4951 (the remainder is 0, so 1 is a divisor of 4951)
4951 / 2 = 2475.5 (the remainder is 1, so 2 is not a divisor of 4951)
4951 / 3 = 1650.3333333333 (the remainder is 1, so 3 is not a divisor of 4951)
...
4951 / 4950 = 1.000202020202 (the remainder is 1, so 4950 is not a divisor of 4951)
4951 / 4951 = 1 (the remainder is 0, so 4951 is a divisor of 4951)

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 4951 (i.e. 70.363342729009). 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 $\frac{N}{d} = D$ )

4951 / 1 = 4951 (the remainder is 0, so 1 and 4951 are divisors of 4951)
4951 / 2 = 2475.5 (the remainder is 1, so 2 is not a divisor of 4951)
4951 / 3 = 1650.3333333333 (the remainder is 1, so 3 is not a divisor of 4951)
...
4951 / 69 = 71.753623188406 (the remainder is 52, so 69 is not a divisor of 4951)
4951 / 70 = 70.728571428571 (the remainder is 51, so 70 is not a divisor of 4951)