jackchang1029 Wrote:Having viewed Ron's video on Prime Box and Tim's explanation above, I am still a bit puzzled on correctly inputting repeated primes of two integers into a PB. Perhaps, an example would better illustrate my question, and I hope you guys can help
If n is divisible by 40 and n is divisible by 20...Primes of 40: 2, 2, 2 and 5
Primes of 20: 2, 2, and 5
Should the Prime Box contain:
2, 2, 2, 5, 5...?
OR2, 2, 2, 5...?
Since I combined a total of four 2's from primes of 40 and 20 and only put two of them in the Prime Box, should I combine the 5 as well? Please help!
Ron's video on PB for those who haven't seen it:
Video I viewed:
http://www.beatthegmat.com/mba/2010/06/ ... rime-boxes
Here's an easy way to think about it. For every distinct prime integer in a prime box, have a contest. Count the number of each integer among the two numbers. Majority wins.
Let me use your example of n which is divisible by 40 and 20:
40=2*2*2*5
20=2*2*5
The first distinct integer is 2. Which number has the most 2s? 40 has three 2s. Thus, n has at least three 2s.
The other distinct integer is 5. Both numbers have one 5, so this one is a tie. Thus, n has at least one 5.
n's prime box must contain 2, 2, 2, 5 as factors, and it may have others. But we know that it definitely has these.
Let's look at another example. Let's say that n is divisible by 12, 27, 50, and 75.
12=2,2,3
27=3,3,3
50=2,5,5
75=3,5,5
2=12 has the most, two. There are at least two 2s that are prime factors of n.
3=27 has the most, three. There are at least three 3s that are prime factors of n.
5=50 and 75 tie with two. There are at least two 5s that are prime factors of n.
Thus, n's prime box must contain:
2,2,3,3,3,5,5 and it could contain other factors.
Hope this makes sense!