This is a question that needs us to convert a number from a decimal base to three other bases
a) Requires to convert 42 decimal to binary or base-2
The most-used method for doing so Is to divide the number by two as many times as needed and collect all the remainders
Start by 42 / 2 = 21. Since 21*2=42, the remainder of the first division is zero.
I'll save that remainder: 0
Now we divide 21/2 to get 10 (only the whole quotient)
Since 10*2=20. There is a remainder here: 21 - 20 = 1
The next division is 10 / 2 = 5. The product 5*2=10 leaves a remainder of 0
Let's go on with the divisions, now we do 5 / 2 = 2. The new remainder is
5 - 2 * 2 = 1
This will be the last division: 2 / 2 = 1 . Remainder 0
The last quotient (1) and the collection of remainders will be joined from last to first:
101010. This is our answer
b) The same procedure goes when converting to base-3
42 / 3 = 14. 42 - 3*14 = 0
14 / 3 = 4, remainder 14 - 4*3 = 2
4 / 3 = 1, remainder 4 - 1 * 3 = 1
Since I cannot divide further the last quotient will be collected as before with the rest:
1120
c) Let's convert to base-5. Follow the same procedure
42 / 5 = 8. Remainder: 42 - 8*5 = 2
8 / 5 = 1. Remainder 8 - 1 * 5 = 3
Cannot divide any more, so I collect the last quotient and the above remainders as:
132
That is our final answer