Perfect Numbers
Definition of a Perfect Number:
A number which is equal to the sum of its factors other than itself is called a perfect number.
Solved Examples:
1. Verify that 6 and 28 are perfect numbers.
Solution:
Factors of 6 are 1, 2, 3,6.
Sum of factors of 6 other than 6 = 1 + 2 + 3 = 6 (number itself).
Factors of 28 are 1, 2, 4, 7, 14, 28.
Sum of factors of 28 other than 28 = 1 + 2 + 4 + 7 + 14 = 28 (number itself).
Thus, 6 and 28 are the perfect numbers. Hence verified.
2. Verify that 496 is a perfect number.
Solution:
Factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
Sum of factors of 496 other than 6 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496 (number itself).
Thus, 496 are the perfect numbers. Hence verified.
You might like these
Highest Common Factor |Find the Highest Common Factor (H.C.F)|Examples
Highest common factor (H.C.F) of two or more numbers is the greatest number which divides each of them exactly. Now we will learn about the method of finding highest common factor (H.C.F). Steps 1: Find all the factors of each given number. Step 2: Find common factors of the
Prime Factorisation |Complete Factorisation |Tree Factorisation Method
Prime factorisation or complete factorisation of the given number is to express a given number as a product of prime factor. When a number is expressed as the product of its prime factors, it is called prime factorization. For example, 6 = 2 × 3. So 2 and 3 are prime factors
Multiples and Factors | Infinite Factors | Multiply Counting Numbers
We will discuss here about multiples and factors and how they are related to each other. Factors of a number are those numbers which can divide the number exactly. For example, 1, 2, 3 and 6 are
Divisible by 3 | Test of Divisibility by 3 |Rules of Divisibility by 3
A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3. Consider the following numbers to find whether the numbers are divisible or not divisible by 3: (i) 54 Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3.
Divisible by 4 | Test of Divisibility by 4 |Rules of Divisibility by 4
A number is divisible by 4 if the number is formed by its digits in ten’s place and unit’s place (i.e. the last two digits on its extreme right side) is divisible by 4. Consider the following numbers which are divisible by 4 or which are divisible by 4, using the test of
Divisible by 5 | Test of divisibility by 5| Rules of Divisibility by 5
Divisible by 5 is discussed below: A number is divisible by 5 if its units place is 0 or 5. Consider the following numbers which are divisible by 5, using the test of divisibility by
Divisible by 6 | Test of Divisibility by 6| Rules of Divisibility by 6
Divisible by 6 is discussed below: A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42
Divisible by 8 | Test of Divisibility by 8 |Rules of Divisibility by 8
Divisible by 8 is discussed below: A number is divisible by 8 if the numbers formed by the last three digits is divisible by 8. Consider the following numbers which are divisible by 8
Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7
Divisible by 7 is discussed below: We need to double the last digit of the number and then subtract it from the remaining number. If the result is divisible by 7, then the original number will also be
Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9
A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:
Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10
Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:
Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple
The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is the smallest of all common multiples.
Multiples | Multiples of a Number |Common Multiple|First Ten Multiples
What are multiples? ‘The product obtained on multiplying two or more whole numbers is called a multiple of that number or the numbers being multiplied.’ We know that when two numbers are multiplied the result is called the product or the multiple of given numbers.
Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples
All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:
Prime and Composite Numbers | Prime Numbers | Composite Numbers
What are the prime and composite numbers? Prime numbers are those numbers which have only two factors 1 and the number itself. Composite numbers are those numbers which have more than two factors.
5th Grade Math Problems
From Perfect Numbers to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb
Oct 21, 24 03:38 PM
Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by -
Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table
Oct 21, 24 02:26 AM
Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times -
Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat
Oct 21, 24 02:16 AM
Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb… -
Concept of Multiplication | What is Multiplication? | Basics Math
Oct 21, 24 01:05 AM
Multiplication is repeated addition of a number to itself. Study the following example to understand it: Example: Take 3 groups of 2 pens each as shown below. How many pens are there in all? -
Properties of Multiplication | Multiplicative Identity | Whole Numbers
Oct 21, 24 12:50 AM
There are six properties of multiplication of whole numbers that will help to solve the problems easily. The six properties of multiplication are Closure Property, Commutative Property, Zero Property…
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.