We have different types of classifications for the numbers: even or odd numbers, natural numbers, real numbers, Prime numbers, and a lot more.
But have you ever heard of perfect numbers is on friendly numbers? Because they exist and have very peculiar and interesting characteristics.
Stay with us until the end and you will be amazed!
What is a perfect number?
perfect number is a sort of sort for a natural number greater than 1, that is, for numbers like .
And how do we check whether a number is perfect or not?
The perfect numbers were called that way by the disciples of the great mathematician Pythagoras, better known as the Pythagoreans.
let's see some examples of those numbers?!
Example: Number 6 is a perfect number. Let's see why:
The natural divisors of the number 6 are: 1, 2, 3, and 6, that is, these are numbers such that when we do the division of 6 by each one of them, we obtain an exact division (rest equal to 0).
Let's add all the proper divisors of 6, that is, add the numbers 1, 2 and 3:
The sum was 6, so 6 is a perfect number.
Now let's see a counterexample, that is, an example of a number that is not a perfect number.
Counterexample: the number 8 no is a perfect number. Look:
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The natural divisors of the number 8 are: 1, 2, 4 and 8.
The sum of the divisors themselves is: , which is different from 8.
So the 8 no is a perfect number.
Finding perfect numbers is not so common as they are rare.. After 6, the next perfect number is 28. Their own divisors are: 1, 2, 4, 7, and 14 (check that their sum is 28).
Then come the numbers: 496, 8.128, 33.550.336 and 8.589.869.056. Notice how many digits this last number has, and it's just the 6th perfect number.
Now, let's see another type of classification, also attributed to the Pythagoreans: that of friendly numbers.
What are friend numbers?
In mathematics, two numbers are called friendly numbers when each of them is equal to the sum of the other's own divisors.
See an example:
Example: Numbers 220 and 284 are friendly numbers.
The 220 proper dividers are: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
The proper dividers of 284 are: 1, 2, 4, 71, 142.
So the numbers 220 and 284 are friendly numbers. Also, know that they are the smallest known friend numbers.
Read too:
- How to write a number in scientific notation? – Changing the comma position and examples
- How to write the numerals 10 to 100 in full
- How to spell out the numerals from 100 to 200
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