Final answer:
To convert the number 407 in base 10 to base 4, divide the number by 4 repeatedly and keep track of the remainders. The remainder of each division will be the corresponding digit in the base 4 representation. The base 4 representation of the number 407 is 6113.
Step-by-step explanation:
To convert the number 407 in base 10 to base 4, we need to divide the number by 4 repeatedly and keep track of the remainder. The remainder of each division will be the corresponding digit in the base 4 representation. Starting with 407, we divide by 4, which gives us a quotient of 101 and a remainder of 3. We repeat this process with the quotient 101, resulting in a quotient of 25 and a remainder of 1. Finally, we divide 25 by 4, resulting in a quotient of 6 and a remainder of 1. Therefore, the base 4 representation of the number 407 is 6113.