Hey!! Do you have any idea about amicable numbers? Just keep in mind 220 and 284 are amicable or you can say friend numbers!! How? That should be the big question. I am now explaining it to you.
See, the factors of 220 are : 1,2,4,5,10,11,20,22,44,55,110
Now if you add them together the summation becomes 284!!
Again, the factors of 284 are: 1,2,4,71,142
If you add them together the summation becomes 220!! Isn't it interesting?
Now, do you know what perfect numbers are?
These are such numbers, the sum of those factors (except the number itself), is equal to the nunber It's elves!!
Example : 6,28,496
The factors of 6 are 1,2,3 and 6. Now if you add 1,2 and 3 the summation becomes 6!!
Again, the factors of 28 are 1,2,4,7,14,28. Niw if you add the factors except 28 it becomes 28!! Same in the case of 496.
Always remember the sequence of prime numbers from 1 to 100. This is
4422-322-321, Total = 25 prime numbers.
Do you know how to recognise a prime numbers??
Let, p be a given number and let n be the smallest counting number such that n^2 >=p. Now test whether p is divisible by any of the prime numbers less than or equal to n. If yes, then p is not Prime number, otherwise p is prime.
Example : let 811. We know that (30)^2 > 811. Now prime numbers less than 30 are 2,3,5,7,11,13,17,19,23,29. Clearly none of this numbers divides 811.
Therefor, 811 is a prime number. Try 137 yourself!!
Again, let 437. We know that (21)^2 > 437. Now prime numbers less than 21 are 2,3,5,7,11,13,17,19. Clearly 437 is divisible by 19. So 437 is not a prime!! Interesting, isn't it??
There is a arithmetic sequence of five numbers!! Can you imagine?
See, 5,11,17,13,29!! The difference is 6 every time? Do you now it before?
So, that's all for today. Play with numbers. It will keep Your brain so active and fresh.
Stay tuned. Happy Numbering. 🧠✍