# Thread: Base 5

1. ## Base 5

Does 124(base 5) represent an odd number? How can you determine whether a number is odd by looking at its base-five representation?

Any takers?

2. Originally Posted by t-lee
Does 124(base 5) represent an odd number? How can you determine whether a number is odd by looking at its base-five representation?

Any takers?
$\displaystyle (124)_5$
Is,
$\displaystyle 1\cdot 5^2 +2\cdot 5^1+4\cdot 1$
Is that even or odd?

3. Hello, t-lee!

Does $\displaystyle 124_5$ represent an odd number? . . . no

How can you determine whether a number is odd by looking at its base-five representation?

Since the base is an odd number, it could be tricky.

But there is a simple rule:
. . Even number of odd digits: even
. . .Odd number of odd digits: odd

4. Originally Posted by Soroban

Since the base is an odd number, it could be tricky.

But there is a simple rule:
. . Even number of odd digits: even
. . .Odd number of odd digits: odd

there is an odd number of odd digits in 124...

5. Originally Posted by Quick
there is an odd number of odd digits in 124...
Yes, which means that $\displaystyle 124_5$ is odd which, in fact, it is. Don't let that 4 on the end fool you. What TPH was trying to say is that
$\displaystyle 1 \cdot 5^2$ is odd
$\displaystyle 2 \cdot 5^1$ is even
$\displaystyle 4 \cdot 5^0$ is even

odd + even + even = odd.

-Dan