### Instruction: What is the base-10 integer 340 when expressed in base 7?### Response: To convert a number from base 10 to base 7, I need to repeatedly divide it by 7 and write down the remainders.
The remainders will form the digits of the base 7 representation, from right to left.
So, let me start by dividing 340 by 7.
Using long division, I get 48 with a remainder of 4.
So the rightmost digit of the base 7 representation is 4.
Next, I divide 48 by 7.
I get 6 with a remainder of 6.
So the second rightmost digit is 6.
Then, I divide 6 by 7.
I get 0 with a remainder of 6.
So the third rightmost digit is 6.
Since I have no more quotient left, I stop the division process.
The base 7 representation is the concatenation of the remainders, from right to left.
So, 340 in base 10 is 664 in base 7.