alternative method

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...

Moved to maths.

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...?

Reply 3

Notnek

21

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'?

Reply 4

DylanJ42

18

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.

Reply 5

Notnek

21

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...