Question

find the sum of even divisors of 4096?​

Answer 1

The number 4,096 can be divided by 13 positive divisors (out of which 12 are even, and 1 is odd). The sum of these divisors (counting 4,096) is 8,191, the average is 6,30.,076.

...

Divisors of 4096.

Answer 2

Answer:

To find the sum of even divisors of 4096, we first need to find all the divisors of 4096.

The prime factorization of 4096 is 2^12, which means that its divisors are all possible combinations of powers of 2, from 2^0 to 2^12.

The even divisors of 4096 are those divisors which have at least one factor of 2, i.e., 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 and 4096.

To find the sum of these even divisors, we can add them up directly:

2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096

= 8190

Therefore, the sum of even divisors of 4096 is 8190.

We can also use a formula to find the sum of divisors of any number n, given its prime factorization. The formula is:

sum of divisors of n = (p1^(a1+1) - 1)/(p1 - 1) * (p2^(a2+1) - 1)/(p2 - 1) * ... * (pk^(ak+1) - 1)/(pk - 1)

where p1, p2, ..., pk are the distinct prime factors of n, and a1, a2, ..., ak are their corresponding powers in the prime factorization.

Using this formula, we can find the sum of divisors of 4096 as:

sum of divisors of 4096 = (2^(12+1) - 1)/(2 - 1) = 8191

View more such questions:

https://brainly.in/question/2645076

#SPJ2