Questions: Write 73 in the base-seven system. 73=□seven

Solution Steps

To convert the decimal number 73 to its base-seven equivalent, we repeatedly divide the number by 7 and record the remainders. The base-seven representation is obtained by reading the remainders in reverse order.

To convert \( 73 \) to base-seven, we start by dividing \( 73 \) by \( 7 \): \[ 73 \div 7 = 10 \quad \text{remainder} \, 3 \] This gives us our first remainder, \( 3 \).

Next, we take the quotient \( 10 \) and divide it by \( 7 \): \[ 10 \div 7 = 1 \quad \text{remainder} \, 3 \] This gives us our second remainder, \( 3 \).

Now, we take the quotient \( 1 \) and divide it by \( 7 \): \[ 1 \div 7 = 0 \quad \text{remainder} \, 1 \] This gives us our final remainder, \( 1 \).

Now, we compile the remainders from the last division to the first:

• Last remainder: \( 1 \)
• Second remainder: \( 3 \)
• First remainder: \( 3 \)

Thus, the base-seven representation of \( 73 \) is \( 133 \).

Final Answer