a number is called a perfect number if it equals the sum of all its factors except itself. for instance , 6 is a perfect number because its factors are 1,2,3 and 6 and 1 + 2 + 3 = 6 .What is the next greater perfect number >
10
Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 10 = 1 + 2 + 3 + 4. This is followed by the perfect numbers
(1+2+3+4+10)/2
20 / 2 = 10
I dont know this question
It is 28
my son is having trouble with a question i'v never heard of heres the question: A perfect number is a number
that equals the sum of its factors, not including
itself. For example, the factors of 28 are 1, 2, 4, 7, 14, and 28.
Because 1 + 2 + 4 + 7 + 14 = 28, 28 is a perfect number.
What are the perfect numbers between 1 and 28?
It is 28 š
To find the next greater perfect number, we need to understand how to identify perfect numbers and then find one that is larger than 6.
Step 1: Identify a perfect number
A perfect number is a positive integer that is equal to the sum of its proper divisors. Proper divisors are the factors of a number excluding the number itself.
Step 2: Find a larger perfect number than 6
We can begin by writing a program or script to calculate the sum of factors for each number. Starting from 7, we will check if the sum of its factors is equal to the number itself. If it is, then we have found a perfect number. If not, we move on to the next number and repeat the process.
Here's a Python code snippet that can help us find the next perfect number after 6:
```python
def calculate_sum_of_factors(n):
# Calculate the sum of factors
factors_sum = 1 # 1 is always a factor of any number
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
factors_sum += i
if n // i != i: # Exclude square factors
factors_sum += n // i
return factors_sum
def find_next_perfect_number(start_from):
next_perfect = start_from + 1
while True:
if calculate_sum_of_factors(next_perfect) == next_perfect:
return next_perfect
next_perfect += 1
# Usage:
next_perfect_number = find_next_perfect_number(6)
print(next_perfect_number)
```
Running this code will output the next perfect number after 6.
Please note that finding perfect numbers beyond a certain point becomes computationally expensive, as higher perfect numbers are quite rare and have very large values.