Question

Which is 243 written as a power of a number?

A.


B.


C.


D.

Answer 1

@satellite73

Answer 2

._. you might wanna look at your options >.>

Answer 3

I can't see what your choices A - D are, but a cheeky answer is 243 = 243^1.

Answer 4

Here's a hint, though. 243 is a multiple of 3.

Answer 5

oh crap sorry lol

Answer 6

3^5 = 243 >_<

Answer 7

here

Answer 8

I'm good :O

Answer 9

Yes you are XD ~ Thankies ~

Answer 10

First, why not do a relatively simple experiment?

Realizing that 243 is an odd number, try odd bases with positive integer exponents to determine whether or not you can arrive at 243.

\[5^{1}=5; 5^{2}=25; 5^{3}=125; and so on.\]

\[3^0=1; 3^1=3; 3^2=9; 3^3=27; and. so .on. \] What happens as you continue to increase the exponents of 3?

Answer 11

He covered it all >_< ^

Answer 12

Later, you might recognize that 243=(3^2)(3^3) = 3^5.

Answer 13

Learning the basic tests for divisibility helps too. I knew that 243 was a multiple of 3 because the digits of the number add to a multiple of 3, i.e. 2+4+3 = 9 = 3x3.

Answer 14

What a neat suggestion, Cliff!

Answer 15

Where'd you pick up that trick?

Answer 16

I usually look at the back of the number and see what its divisible by

Answer 17

4th grade, I think . .

Answer 18

I discovered a few others on my own. I now know how to test for divisibility of all numbers up to and including 12. I understand the general method for testing prime numbers greater than 12, but it's pretty complicated.

Answer 19

Here's a cool one for divisibility by 11. The sum of every-other digit minus the sum of the other digits is a multiple of 11.

e.g. 12705 - take 1+7+5 and subtract 2+0 and 13-2 is 11, so 12705 is divisible by 11.

Answer 20

What about 5,896,547 o.0

Answer 21

It's not divisible by 3 or 11 (or any even number, of course). Not divisible by 5.., Doesn't appear to be divisible by 7 either, so I'd have to test some two-digit prime numbers next

Answer 22

5896547 is divisible by 43.

Answer 23

Cliff, I'm really impressed. I've made and am saving copies of this dialogue for later ref. Thanks.

Answer 24

If you get a chance to study some number theory, especially modular arithmetic, it'll make more sense.

Answer 25

Oh, and 5896547 is also divisible by 241 and 569.

Answer 26

I really do need to express my reactions to those last few statements: WOW!

Answer 27

Dayummm >_<

Answer 28

In the spirit of full disclosure, I found 241 and 569 by brute force, not any number theory trick.

Answer 29

Brute force is a program I used to decode games and modify them >.> didn't know that

Answer 30

The term, "brute force" just refers to using the fast processing speed of a computer to grind out calculations. I wrote a quick program to iterate factor-finding calculations until it hit on a couple.

Answer 31

ah