# Remainder of a number

1. Aug 1, 2010

### thereddevils

1. The problem statement, all variables and given/known data

How much is the balance if u want to get integer value of ((2^1000) divided by 7))

2. Relevant equations

3. The attempt at a solution

I need a little hint to start off with an attempt.

2. Aug 1, 2010

### HallsofIvy

Staff Emeritus
Since that is a rather large power of two, I suggest that you start with simple examples and see if you can find a pattern:

$2^0= 1$. Remainder on division by 7: 1
$2^1= 2$. Remainder on division by 7: 2
$2^2= 4$. Remainder on division by 7: 4
$2^3= 8$. Remainder on division by 7: 1
$2^4= 16$. Remainder on division by 7: 2
$2^5= 32$. Remainder on division by 7: 4
$2^6= 64$. Remainder on division by 7: 1
$2^7= 128$. Remainder on division by 7: 2
$2^8= 256$. Remainder on division by 7: 4

Get the idea?

3. Aug 1, 2010

### thereddevils

Thanks Hallsofivy!