FUN WITH ANY THREE DIGIT WHOLE NUMBER.

Here we have an interesting property of any three digit whole number.
Take any three digit whole number.
For example:   935
Repeat the digits and write to the next to the above number.
935935.
The original number became a six digit number.
When such six digit number is divided by  1001 we get the answer     935
Other examples:

738738÷1001=738
135135÷1001=135
777777÷1001=777

This trick is applicable to any three digit whole number.

Note :-Prime factors of 1001 are7,13,and 11.
Any such six digit whole number  is divisible by 7,11,13,77,91,143,and1001.

Amusing Property Of Three Consecutive Numbers.

For any three consecutive numbers product of the first and the last number plus one is equal to the square of the middle number.

Step 1:- Take any three consecutive three numbers.
For example—2, 3, 4

Step 2:- Product of the first and the last number.
Here, 2*4=8

Step 3:- Add one to the product of step 2
8+1=9

Step 4:- Result of Step #3 is the square of the middle number.
that is , Square of three is equal to nine.

Another example,
Suppose three consecutive numbers are 8,9,10.
As  above mentioned,
8*10+1=81.
81 is equal to the square of 9.


Take more examples and think how it works. Enjoy it!

Note for Parents /Teachers:
This way you are introducing your child to formula (a+1)²=a(a+2)+1

Strange Squares

Some pairs of square numbers have a strange property .

For example, Take a pair of 144 and make reverse of it i.e. 441 .
144 is a square of 12 (12 *12 = 144)
441 is a square of 21 (21*21 = 441)

Here 12 and 21 are reverse numbers . and same with their square numbers (144 and 441) .

Another Example is , pair of 169 and 961 .
169 is a square of 13 (i.e. 13 * 13 = 169 )
961 is a square of 31 (i.e. 31 * 31 = 961 )

Here 13 and 31 are reverse numbers . and same with their square numbers (169 and 961) .

If you observe carefully , you will find only two numbers in two digits which has this combinations .

For three digit numbers , 112 and 211 is the combination .

Square of 112 ( i.e. 112 *112) is 12544
Square of 211 ( i.e. 211 *211) is 44521

Can you find any other pairs like this ?