Question

what is the result when 2is successively divided by 2 5 times

Answer 1

us say the number in the question as x. Now, from the first situation we shall try to build some properties of this number.

1. The number x is divisible by 5.

2. y = x/5 is odd in nature.

put 1 and 2 to get

x/5 = 2n + 1 = y

x = 5 (2n + 1)

x = 10n + 5

That gives some clue about this number of ours, narrowing down the set down to odd multiples of 5. Moving on, we have-

3. (y / 2) - 2 is divisible by 3.

( ( (y - 1) / 2 ) - 2) / 3 = z; z is any integer

( (y - 1) / 2 ) - 2 = 3z

(y - 1)/ 2 = 3z + 2

y - 1 = 2 (3z + 2)

y - 1= 6z + 4

y = 3 (2z + 1) + 2

y = 3m + 2

Also, we have y as an odd number which means the 'm' in '3m' term should be odd which is also evident from m = 2z + 1 form.

we have

x = 30z + 25

Thus, we get our set of numbers as

A= { x | x = 30z + 25; z is a positive integer}

A = { 25, 55, 85, ... }

Now, getting back to the question take any of these numbers and divide them sequentially to get answer to the question or just work with the general form. :)

hope it helps you

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