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Comment on GCD of x and y is 12
what if the question asks for
Hi Mohammad,
Hi Mohammad,
Then we have....
METHOD 1:
x = 12 and y = 12 meets the condition that the GCD of x and y is 12
Here, 2x = (2)(12) = 24
And 3y = (3)(12) = 36
So, the GCD of 2x and 3y = the GCD of 24 and 36
= 12
METHOD 2:
2x = (2)(2)(2)(3)(?)(?).....
3y = (3)(2)(2)(3)(?)(?).....
We can see that 2x and 3y have two 2's and one 3 in common.
So, the GCD of 2x and 3y = (2)(2)(3) = 12
Cheers,
Brent
Hi, Brent!
What if the initial values of x and y are 12 and 24, respectively, not 12 and 12. If we need to find GCD for 2x and 2y. I got 24, not 12. What did i wrong?
Thank you in advance!
Hi Lidiia,
Hi Lidiia,
But the correct answer IS 24 (not 12)
As long as we choose two numbers that satisfy the given condition (GCD of x and y is 12), then we will arrive at the correct answer.
12 and 24 have a GCD of 12.
So, we can let x = 12 and y = 24
We want to find the GCD for 2x and 2y
2x = (2)(12) = 24
2y = (2)(24) = 48
The GCD of 24 and 48 is 24.
Answer: D
Cheers,
Brent
I’m sorry, I meant 2x and 3y,
Sorry, you originally wrote
Sorry, you originally wrote "2x and 3y", but I thought it was a typo. So, I edited your question.
You're creating a different question altogether then. I believe you're asking:
If the GCD of x and y is 12, what is the GCD of 2x and 3y
In this case, there is not one unique answer. Consider these two cases.
CASE A: x = 12 and y = 12. Here, the GCD of 2x and 3y is 12
CASE B: x = 12 and y = 24. Here, the GCD of 2x and 3y is 24
Does that answer your question?
Cheers,
Brent
Yes, that was my question.
Can you clarify why for the
Let me know if my question is unclear.
Two numbers can share more
Two numbers can share more than one of each prime.
Unfortunately, the examples used in the previous video lesson never shared more than one of each prime.
Let's examine some examples in which the numbers share more than one of a certain prime.
100 = (2)(2)(5)(5)
75 = (3)(5)(5)
Here, 100 and 75 share two 5's
(5)(5) = 25
So, the GCD of 100 and 75 is 25
540 = (2)(2)(3)(3)(3)(5)
1575 = (3)(3)(5)(5)(7)
Here, 540 and 1575 share two 3's and one 5
(3)(3)(5) = 45
So, the GCD of 540 and 1575 is 45
4800 = (2)(2)(2)(2)(2)(2)(3)(5)(5)
16016 = (2)(2)(2)(2)(7)(11)(13)
Here, 4800 and 16016 share four 2's
(2)(2)(2)(2) = 16
So, the GCD of 4800 and 16016 is 16
I hope that helps
Ah, yes it does! Thank you!
actually for this question
let's say 12 and 24, so 24 and 48, GCD 24
Does this work?
Yes, that definitely works.
Yes, that definitely works. That's the first approach covered in the solution.