Solve Exponents Question: 333333/33 Remainder Value

[TheExibo]

If you divide 333³³³ by 33, what is the value of the remainder?

I'm not sure where to starte since this number can't be put into a calculator. Is there something with logs? I was thinking of bringing the number down with logs to 333log333, but I'm confused as to where that will lead me.

 

[jedishrfu]

Write 333 in prime number factors and see if that helps.

 

[HallsofIvy]

If you divide 333³³³ by 33, what is the value of the remainder?

I'm not sure where to starte since this number can't be put into a calculator. Is there something with logs? I was thinking of bringing the number down with logs to 333log333, but I'm confused as to where that will lead me.

Taking the logarithm of $333^{333}$, divided by 3, would give 333log(333)- log(3). The difficulty is that your calculator can only give a limited number of decimal places for the logarithm and multiplying by 333, then taking the exponential of the result, will make the "round off error" worse.

 

[micromass]

Do you know modulo arithmetic? You should look into that. (It's not very difficult, it's mainly just a handy notational system to make problems like these easier)