What are the divisors of 2948?

1, 2, 4, 11, 22, 44, 67, 134, 268, 737, 1474, 2948

There is a total of 12 positive divisors.
The sum of these divisors is 5712.
The arithmetic mean is 476.

8 even divisors

2, 4, 22, 44, 134, 268, 1474, 2948

4 odd divisors

1, 11, 67, 737

How to compute the divisors of 2948?

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 2948 by each of the numbers from 1 to 2948 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)

2948 / 1 = 2948 (the remainder is 0, so 1 is a divisor of 2948)
2948 / 2 = 1474 (the remainder is 0, so 2 is a divisor of 2948)
2948 / 3 = 982.66666666667 (the remainder is 2, so 3 is not a divisor of 2948)
...
2948 / 2947 = 1.0003393281303 (the remainder is 1, so 2947 is not a divisor of 2948)
2948 / 2948 = 1 (the remainder is 0, so 2948 is a divisor of 2948)

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 2948 (i.e. 54.295487841993). 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 $\frac{N}{d} = D$ )

2948 / 1 = 2948 (the remainder is 0, so 1 and 2948 are divisors of 2948)
2948 / 2 = 1474 (the remainder is 0, so 2 and 1474 are divisors of 2948)
2948 / 3 = 982.66666666667 (the remainder is 2, so 3 is not a divisor of 2948)
...
2948 / 53 = 55.622641509434 (the remainder is 33, so 53 is not a divisor of 2948)
2948 / 54 = 54.592592592593 (the remainder is 32, so 54 is not a divisor of 2948)