# Calculate 3310base 5 - 1442base 5

+1 vote

It’s base number problem.

First convert base 5 to base 10.

33105 = (3 · 53+ 3 · 52+ 1 · 51 + 0  · 50)10 = 45510

14425 = (1 · 53+ 4 · 52+ 4 · 51 + 2  · 50)10 = 24710

33105 -  14425 =  45510  - 24710 = 20810

Next Convert base 208 base 10 into base 5.

208 = a0 + 5a1 + 25a2 + 125 a3 + 625 a4 + 3125a5.

where all the are ai digits from 0 to 4. Obviously, all the ai from a4 and up  are 0 since otherwise they will add in a number greater than 208, and all the terms in the sum are nonnegative. Then, we wish to find the largest a3 such that 125a3 does not exceed 208. Thus, a3 = 1 since 1a3 = 125 and 2a3 = 250.

This leaves us with 208 = a0 + 5a1 + 25a2 + 125(1) à 83 = a0 + 5a1 + 25a2

83 = a0 + 5a1 + 25(3)à 8 = a0 + 5a1

8 = a0 + 5 (1) à a0 = 3

a0  = 3, a1  = 1, a2  = 3 and a3 = 1

208 10= 13135.

Let's check by converting answer back into base 10. We know that

13135 = (1 · 53+ 3 · 52+ 1 · 51 + 3 · 50)10 = 125 + 75 + 5 + 3 = 208.

33105  - 14425 = 208 10= 13135.

I hope it helps a lil.