Number base five to base eight

Question

How to convert 434 base five to base eight?

Answer 1

First to base 10: (4*125)+(3*25)+4 = 595

Now convert to base 8...divide successive remainders to get 1123=(1*512)+(1*64)+(2*8)+3

Answer 2

Think about the base 10 number system. We have columns for 1s, 10s, 100s, 1000s, etc. As we move to the left we add another column that is 10 times the previous column. The same is true for other bases below base 10 (above base 10 letters are used, but that's not important right now).

For a base 5 system we would have columns for 1s, 5s, 25s, 125s, etc. So 434 base 5 would be

25s 5s 1s

4 3 4

So it would be 4* 25 + 3*5 + 4*1 = 119 in base 10

To convert this to base 8 we would have columns for 1s, 8s, 64s, Now we can figure out what 119 base 10 is in base 8

64 goes into 119 once, so there would be 1 64 with a remainder of 119-64 = 55

64s 8s 1s

1

8 goes into 55 6 times, so there would be 6 8s with a remainder of 55-48 = 7

64s 8s 1s

1 6

And that would leave 7 1s

64s 8s 1s

1 6 7

So 434 base 5 would be 167 base 8, and both would be 119 base 10