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rock_mit182

  • one year ago

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 :

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  1. rock_mit182
    • one year ago
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    \[m = p ^{b} q^{a} r ^{c}\] \[n = p^{a}q^{c}r^{b}\]

  2. rock_mit182
    • one year ago
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    @paki @Luigi0210

  3. rock_mit182
    • one year ago
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    @misty1212 @calculusxy plz how do i solve this ?

  4. rock_mit182
    • one year ago
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    @IrishBoy123

  5. IrishBoy123
    • one year ago
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    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?

  6. IrishBoy123
    • one year ago
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    oh! there are some proper mathematicians watching now i reckon they'll do this better than me :-)

  7. rock_mit182
    • one year ago
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    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. \[p^{a}q^{c}c^{b}\]

  8. misty1212
    • one year ago
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    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 \(7^2\)

  9. misty1212
    • one year ago
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    in other words, just like with actual numbers, pick the lowest exponent

  10. rock_mit182
    • one year ago
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    so it the answert is c because that expression has the lowest exponents ?

  11. rock_mit182
    • one year ago
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    altought it would be a lot alike to a -.-

  12. rock_mit182
    • one year ago
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    i guess it is C after all they have the lowest common exponents of m and n

  13. rock_mit182
    • one year ago
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    anyway thanks to all of you :)

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