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 2 | Test of Divisibility by 2 |Rules of Divisibility by 2
A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.
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:
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
-
Worksheet on 10 Times Table | Printable Multiplication Table | Video
Mar 21, 25 03:46 PM
Worksheet on 10 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home. -
5th Grade Prime and Composite Numbers | Definitions | Examples | Math
Mar 21, 25 12:18 AM
5th grade prime and composite numbers -
14 Times Table | Read and Write Multiplication Table of 14| Video
Mar 20, 25 04:03 PM
In 14 times table we will learn how to read and write multiplication table of 14. We read fourteen times table as:One time fourteen is 14 Two times fourteen are 28 Three times fourteen are 42 -
5th Grade Test of Divisibility Rules | Divisibility Rules From 2 to 12
Mar 20, 25 04:00 PM
In 5th grade test of divisibility rules we will learn about the exact divisibility of a number by the numbers from 2 to 12. The digit in the ones place should be 2, 4, 6, 8 or 0. -
5th Grade Even and Odd Numbers | Definitions | Examples
Mar 20, 25 02:45 AM
Numbers which are exactly divisible by 2 are even numbers. For example. 2,4,6,8,20,48,88, etc. are even numbers. They are multiples of 2. Numbers which are not exactly divisible by 2 are odd numbers…
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.