Question

whats the trick to find remainder of 2^14/7

Answer 1

hint : `2^3/7` leaves the remainder `1`

Answer 2

\[\large 2^{14} = 2^{3*4 + 2} = 4*8^4 \equiv 4*1^4 \equiv 4 \]

Answer 3

thats one way ^^
heard of Fermat's little theorem ? :)

Answer 4

no

Answer 5

Okay, then just use the earlier method...
did u get how/why 8 became 1 ?

Answer 6

\[\large 2^{14} = 2^{3*4 + 2} = 4*\color{red}{8}^4 \equiv 4*\color{red}{1}^4 \equiv 4\]

Answer 7

yes (7+1)/7 gives remainder 1

Answer 8

Correct !

Answer 9

another way to look at :\[\large 8^4 = (7+1)^4 \]

familiar with binomial expansion ?

Answer 10

You might find this useful later in life
http://vikhyat.net/blog/archives/2011/03/30/remainder-when-dividing-large-numbers/