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1. Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
2. Moved to maths.
3. (Original post by neharajput)
Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
How does 108 and 36 have a common factor of 216 and 540...?
4. (Original post by neharajput)
Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
Should that word be 'are'?
5. (Original post by neharajput)
Two numbers are common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
My method;

Let A = numbers required

first acknowledge that A is a multiple of 9 and 12

L.C.M. of 9 & 12 = 36

therefore A takes the form 36n (where n is > 0 and an integer)

then think about the multiples of A, 540 and 216

540 / 36 = 15
216 / 36 = 6

therefore n must be a factor of both 15 and 6

n = 1 and 3 only

therefore A = 36(1) and 36(3) = 36 and 108

as required.
6. (Original post by neharajput)
Two numbers have common factors of 216 and 540 and are multiples of 9 and 12. What are these two numbers? I can answer this question and figure out the answer as being 108 and 36, but my method is quite long, which is why I was wondering how other people would go out answering the question...
Assuming a typo, this question becomes a lot simpler if you write each number as products of their prime factors.

Have you tried this?
7. (Original post by Zacken)
How does 108 and 36 have a common factor of 216 and 540...?
I accidentally typed have, but I meant to say are

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