SOLUTION: In What postive base B does the equation 4*12=103 for multiplication of base B hold?

Question 30471: In What postive base B does the equation 4*12=103 for multiplication of base B hold?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
the answer is base 5.

I am not sure if there is a "proper" way of figuring this out, using "modulo" maths, but here is my approach:

12
x4
__

In base 10, we would say... what is 2x4? answer is 8.

In our base, the answer is still "8", but we will write it differently.

Seeing as how we have the number 4, the base must be base 4 or greater, so i started there:

base 4, the number 8 would be 20...no end "3" there. So, base 5...

base 5, the number "8" would be 13.. voila, a "3". So base 5 looks a good guess.

so, 2x4 is "8"...written as 3 with the 1 carried.

Now, 1x4 is 4 plus the carried 1 is 5. In base 5, 5 is written as "10"

So we have "10"..."3" --> 103.

Hope this explains it well enough for you.

jon.

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