What is the least possible value that can be subtracted from 2^586 so that the result is a multiple of 7? Select.
A) 2
B) 3
C) 5
D) 7
E) 11
We need to subtract something to make 2^586 a multiple of 7.   So let us try to write 2^586 in a from from which we can convert it in terms of 7   We know that 2^3 = 8 and 8 = (7+1)   Hence we will write 2^586 in powers of 8   2^586 = 2*2^585 = 2*8^195 = 2*(7+1)^195   2ll of the terms of (7+1)^195 will be multiple of 7 apart from the last term - "1"   Hence 2*(7+1)^195 = 2(Multiples of 7 + 1) = 2*Multiples of 7 + 2   Therefore we need to subtract 2 to make 2^586 a multiple of 7   2NSWER:2
<result>A</result>
What is the least possible value that can be subtracted from 2^586 so that the result is a multiple of 7?