Perfect number, co-prime number and twin primes — lesson. Mathematics State Board, Class 6.

PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

Book Free Demo

A perfect number is defined as a number for which the sum of all its factors is equal to twice the number.

Example:

Let's take the factors of

$6$ are

$1$ ,

$2$ ,

$3$ and

$6$ .

Then the sum of the factors becomes:

$1+2+3+6=12 =12 \times6$

Therefore,

$6$ is a perfect number.

Likewise the factors of

$6$ , we take the factors of

$496$ are

$1$ ,

$2$ ,

$4$ ,

$8$ ,

$16$ ,

$31$ ,

$62$ ,

$124$ ,

$248$ and

$496$ .

$1+2+4+8+16+31+62+124+248+496$

$= 992$

$=2\times 496$

Therefore,

$496$ is a perfect number.

A co-prime number is a number with any set of numbers that do not have any other common factor other than

$1$ . It is also known as relatively prime numbers.

Example:

Factors of

$5 =$

$1$ ,

$5$ .

Factors of

$6 =$

$1$ ,

$2$ ,

$3$ ,

$6$ .

These two numbers show that

$5$ and

$6$ have no common factor other than 1.

Therefore, they are co-prime numbers.

Properties of co-prime numbers:

All prime numbers are co-prime to each other.
Any consecutive whole numbers are always co-primed.
Sum of any two co-prime numbers is always co-primed.
Co-prime numbers need not be prime numbers.

Twin primes are a pair of primes that differ by

$2$ .

First few twin primes are

$(3, 5); (5, 7); (11, 13); (17, 19); (29, 31); (41, 43)$ .

Example:

Express

$44$ as the sum of two odd primes.

Here we have to find

$2$ numbers which are odd as well as prime numbers.

And whose sum is

$44$ .

Odd prime numbers upto

$44$ are

$3$ ,

$5$ ,

$7$ ,

$11$ ,

$13$ ,

$17$ ,

$19$ ,

$23$ ,

$29$ ,

$31$ ,

$37$ ,

$41$ ,

$43$ .

Now let’s find out a pair of numbers whose sum is

$44$ . Sum of

$3$ and

$41$ is

$44$ .

So,

$44 = 3 + 41$ .

Previous theory

Exit to the topic

Next exercise

Send feedback

Did you find an error?

Send it to us!

7. Perfect number, co-prime number and twin primes

Theory: