# Why Is 16 a Near Perfect Number?

August 14, 2022

By a near-perfect number, we mean a number n whose sum of positive divisors excluding n is n-1. For example, 16 is a near-perfect number.

## Why is 16 a perfect number?

Perfect numbers are numbers that are equal to the sum of all their divisors, excluding themselves.

## What is a near perfect number in math?

We call n a near-perfect number if n is the sum of all of its proper divisors except one of them, which we call the redundant divisor. For example, the plot 12 = 1 + 2 + 3 + 6 shows that 12 with the redundant divider 4 is almost perfect.

## What makes a perfect number perfect?

perfect number, a positive integer equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers include 28, 496, and 8,128.

## Is 16 a perfect square?

Informally, when you multiply an integer (an “whole” number, positive, negative, or zero) by itself, the resulting product is called a square number, or a perfect square, or simply “a square.” So 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, etc. are all square numbers.

## Who invented perfect numbers?

The story of perfect numbers began over 2300 years ago in one of the most influential mathematical works ever published: The Elements. The around 300 B.C. Born the Greek mathematician Euclid founded the study of perfect numbers as a teacher in Alexandria under the reign of Ptolemy I.

## What is a near number?

More importantly, the near-numbers are a set of concrete mathematical objects that provide a framework both for building an accurate intuitive understanding of the limit concept and for connecting that understanding to the formal definition of the limit< /b>.

## Why is 6 a perfect number?

A perfect number is a positive integer that is equal to the sum of its proper divisors, excluding the number itself. For example, 6 is a perfect number because the proper divisors of 6 are 1, 2, and 3, and 6 =1+2+3. This is also known as the aliquot sum. Other perfect numbers are 28, 496, and 8,128.

## Why is 28 a perfect number?

A number is perfect when all of its factors, including but excluding 1, add up perfectly to the number you started with. For example, 6 is perfect because its factors—3, 2, and 1—all add up to 6. 28 is also perfect: 14, 7, 4, 2 and 1 add up to 28.

## Is 16 a perfect number?

It is known that all even perfect numbers (except 6) end in 16, 28, 36, 56, 76, or 96 (Lucas 1891) and have the digital root 1. Specifically, the last digits of the first few perfect numbers are 6, 8, 6, 8, 6, 6, 8, 8, 6, 6, 8, 8, 6, 8, 8, …

## Why is 1, 2 the perfect number?

Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there is a subset of the correct divisors of 12 that add up to 12 (excluding all but 4), 12 is a semiperfect number.

## Is 14 a perfect number?

Checking for perfect numbers:

Without the number itself, the sum of these factors is 1 + 2 + 4 + 7+ 14 = 28. Since the sum of the factors is equal to the number itself, we call a perfect number.

## Why is 10 a perfect number?

A perfect number is a positive integer that satisfies the following property: The sum of all proper divisors of the number (excluding itself) is equal to this number.

## Why Is 9 the perfect number?

The number 9 is revered in Hinduism and is considered a complete, perfect and divine number because it represents the end of a cycle in the decimal system that began as early as 3000 BC. on the Indian subcontinent.

### References:

2. https://www.sciencedirect.com/science/article/pii/S0022314X12002041
4. https://www.britannica.com/science/perfect-number
5. https://elementarymath.edc.org/resources/square-number/
6. https://plus.maths.org/content/bizarre-definition-perfect
7. https://arxiv.org/abs/math/0412157
8. https://www.greaterkashmir.com/todays-paper/six-is-perfect
9. https://www.forbes.com/sites/startswithabang/2018/06/28/celebrate-the-math-holiday-of-perfect-number-day-this-june-28th/
10. https://mathworld.wolfram.com/PerfectNumber.html
11. https://en.wikipedia.org/wiki/12_(number)