how 598^19 is an odd number?

Question

It was a question asked by someone..
http://answers.yahoo.com/question/index?qid=20061207182048AAD7xgM&r=w#EsInW2DoADM76ecn4xv6qjRZ3zbwRe75iN1Gr0sylvXq6WFPBLPG

and, most people got "1" as the last digit for the answer.

but i never figured out, how even that's possible?

umm, is there any reason, why three people come up with same answer?

thanks, yea.. i almost missed that thing!!!
and, fudged about that ...

Answer 1

It's not an odd number.


The last digit will continue to go in a 4, 2, 6, 8, 4 pattern.

Maybe they tried to do it on a calculator. The number is far too large to be read on a calculator without scientific notation, thus some of the numbers are cut off.


edit: it is your mistake here. Their question was 19^598, which is not the same as 598^19 ;)

Answer 2

598^19 =
598 x 598 x 598 x 598 x 598 x 598 x
598 x 598 x 598 x 598 x 598 x 598 x
598 x 598 x 598 x 598 x 598 x 598 x 598

Now group up fot 598 x 598 x 598 = 213847192

213847192 x 213847192 x
213847192 x 213847192 x
213847192 x 213847192 x 598

now see 2 x 2 x 2 x 2 x 2 x 2 x 8 = even number

The anwer that you linked to has a typo, they found that:

598 x 598 x 598 = 213847129 instead of 213847192

Answer 3

The original question asked for 19^598, not 598^19. It's just that some of the answerers started started answering 598^19. It is indeed true that 19^598 has 1 as its last digit. Cheers!

As a note, it goes to show how important it is for answerers to thoroughly read the question and all references provided ;)

Answer 4

It is not possible.

598^19 = (2*249)^19= 2 * [(2^18) * (249^19)]

2 times ANY integer is an even integer, by definition, since even numbers are divisible by 2.

Done.

However, 19^598 is odd, since 19 is odd, and odds multiplied by odds are likewise always odd. Remember that an odd number cannot contain a factor of 2. Thus no number of odds multiplied by one another can ever have a factor of two, and so, cannot be even.

Answer 5

since 598 is an even number 598^19 is an even number. Not an odd number

Answer 6

The question asked "What is 19 to the power 598?" which means 19^598 (not 598^19).

598^19 is, of course, even.

Answer 7

It's an even number. If I multiply 598 or any
even number by itself any number of times
I still get an even number!

Answer 8

298^19 (read as "298 to the power of 19") is an even integer, but
19^298 (read as "19 to the power of 298") is an odd integer.

I think you misinterpret the wording of the problem.

^_^

Answer 9

An even number times any number is always even. An even number raised to any power is even.

Answer 10

it is an even number