Is 5 a divisor of 3^444 or 4^333?

[Natasha1]

Without using a calculator, how can I know if 5 is a divisor of 3^444 and/or 4^333?

 

[matt grime]

Fermat's Little theorem, how else can you say anything about anything?

 

[Manchot]

Did you learn about prime factorization in grade school?

 

[matt grime]

true, i misread it.

 

[Natasha1]

Did you learn about prime factorization in grade school?

No...

 

[HallsofIvy]

Well, you should have! Any number can be written, in a unique way, as a product of primes. How would 3⁴⁴⁴ be written as a product of primes? Any 5s in there? (Hint: 3 and 5 are prime numbers.)

How would 4³³³ be written as a product of primes? (Hint: 4 is not a prime number but 2 is.)