Question

How would I reduce 540/600 using prime factorization?

Answer 1

$540|2\\270|2\\135|5\\.\ 27|3\\.\ \ 9|3\\.\ \ 3|3\\.\ \ 1|\\540=2\times2\times5\times3\times3\times3\\\\600|2\\300|2\\150|2\\.\ 75|3\\.\ 25|5\\.\ \ 5|5\\.\ \ 1|\\600=2\times2\times2\times3\times5\times5$


$\frac{540}{600}=\frac{2\times2\times5\times3\times3\times3}{2\times2\times2\times3\times5\times5}=\frac{3\times3}{2\times5}=\frac{9}{10}$

Answer 2

First you would see the biggest common factor in between 540 and 600. Here is a trick: to know if you have a factor of 3, you add the numbers of that number, then see if it is dividable by 3. So for number 540: 5+4+0=9. 9/3=3. So 540/3= 180. and for 600: 6+0+0=6. 6/3=2. 600/3=200. Now u have 180/200. divide that by 10 and u get 18/20. and finally you divide that by 2 and you get 9/10. Now the numbers i divided 540/600 we 3, 10 and 2. Numbers 3 and two are prime factors cause u cant divide them anymore unless u get 1 or a decimal number but number 10 is not prime since you can divide that by 2 witch will give you 5. So the prime factors of 540/600 are 2, 2, 3 and 5. 9/10