### Instruction: What is the base-10 integer 340 when expressed in base 7?### Response: To express a number in a different base, I need to divide it by the base repeatedly and write down the remainders.
The remainders will form the digits of the number in the new base, starting from the rightmost one.
So I start by dividing 340 by 7 and getting a quotient of 48 and a remainder of 4.
That means the rightmost digit in base 7 is 4.
Then I divide 48 by 7 and get a quotient of 6 and a remainder of 6.
That means the next digit in base 7 is 6.
Then I divide 6 by 7 and get a quotient of 0 and a remainder of 6.
That means the next digit in base 7 is 6 again, and since the quotient is 0, I'm done.
So the number 340 in base 10 is 664 in base 7.