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 (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 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
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
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.
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 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 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 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 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
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 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:
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.
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.
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:
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 Numbers Page
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.
Share this page:
What’s this?


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.