Question

Find GCD(-27,-45).

I think that the answer is 9, but the back of the book says 3. Which do you think is correct and why?

Answer 1

what are their prime factors?

Answer 2

i dont think ive got this scripted for negative numbers ... so it might be best to enter them in absolute form

Answer 3

Well I believe that with negative numbers, it is still the highest positive factor (which would be 9). I'm just not completely sure.

Answer 4

you are correct, i just didnt have my scripting for the program to account for negative entries :)

Answer 5

if -9 is a factor, then so is +9, and +9 is greater then -9

Answer 6

Do you know how to find the prime factorization of a number?

Answer 7

i find prime factors like a type ... hunt and peck :)

Answer 8

@Skip2mylou426 ?

Answer 9

I thought so until I hit number theory haha

Answer 10

Divide by the prime numbers in order as many times as possible before going on to the next prime.

Answer 11

I don't think it's asking for primes, I'm pretty sure it's just asking for the GCD

Answer 12

Oops I meant the GCD is the GCF, right?

Answer 13

if d|a and d|b then d is a common divisor

the largest common divisor is the GCD (greatest common divisor)

Answer 14

That's why I think it's 9, but I can't figure out why the back of the book says 3. That makes no sense to me.

Answer 15

3 | -27 and -45

9 | -27 and -45

since 9 > 3, 9 is the gcd

Answer 16

make sure your looking at the correct answer solution :)

Answer 17

45 = 27(1) + 18
27 = 18(1) + 9 <-- gcd is 9
18 = 9(2) + 0

Answer 18

Maybe it's a typo that should have been 3^2?

Answer 19

if you haven't noticed, you will, that math books often have typos
proof readers have a hard time picking up mistakes.

You can use wolfram as a check on some of these questions
http://www.wolframalpha.com/input/?i=gcd%28-27%2C-45%29

Answer 20

Yes, even the best ones aren't typo-free.

Answer 21

"The positive divisors of 27 are 1, 3, 9, and 27. The positive divisors of 45
are 1, 3, 5, 9, 15, and 45. It follows that the greatest positive divisor of 27 and 45 is 3."

Answer 22

I was thinking that it might be a typo, but I'm looking at their lists and it's just not making sense. I'm gonna stick with 9. Thanks for your input everyone!

Answer 23

good luck ;)