rock_mit182
  • rock_mit182
p, q and r are different prime numbers; a,b and c are positive whole numbers, such as a>b>c; if n = p ^{a} q^{c} r^{b} and m = p ^{b} q^{a} r^{c}, then the greatest common divisor of m and n is :
Mathematics
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SOLVED
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chestercat
  • chestercat
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rock_mit182
  • rock_mit182
\[m = p ^{b} q^{a} r ^{c}\] \[n = p^{a}q^{c}r^{b}\]
rock_mit182
  • rock_mit182
@paki @Luigi0210
rock_mit182
  • rock_mit182
@misty1212 @calculusxy plz how do i solve this ?

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rock_mit182
  • rock_mit182
@IrishBoy123
IrishBoy123
  • IrishBoy123
to illustrate with a simpler problem let's say you have \(2^3 \ 3^5\) and \(2^5 \ 3^2\) then you would go with \(2^3 \ 3^2\) the lowest exponent in each case because 2 and 3 are prime does that help?
IrishBoy123
  • IrishBoy123
oh! there are some proper mathematicians watching now i reckon they'll do this better than me :-)
rock_mit182
  • rock_mit182
the options are: a.\[p^{c}q^{b}c^{c}\] b.\[p^{b}q^{b }c^{c}\] c. \[p^{b}q^{c}c^{c}\] d. \[p^{a}q^{c}c^{b}\]
misty1212
  • misty1212
lol here is another hint: since \(a>b\) the greatest common divisor of \(p^a,p^b\) is \(p^b\) just like the greatest common divisor of \(7^3\) and \(7^2\) is \(7^2\)
misty1212
  • misty1212
in other words, just like with actual numbers, pick the lowest exponent
rock_mit182
  • rock_mit182
so it the answert is c because that expression has the lowest exponents ?
rock_mit182
  • rock_mit182
altought it would be a lot alike to a -.-
rock_mit182
  • rock_mit182
i guess it is C after all they have the lowest common exponents of m and n
rock_mit182
  • rock_mit182
anyway thanks to all of you :)

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