+13 A store would like to set up fish tanks that contain equal numbers of angle fish, sword fish, and guppies. What is the greatest number of tanks that can be set up if the store has 12 angle fish, 24 sword fish, and 30 guppies?
+399 The GCF for \(30, 24,\) and \(12\) is \(6\). This means that there will be \(6\) tanks. (Correct me if I'm wrong, I'm not so sure about this one. I may have read it wrong).
- Daisy
+4620 GCF common factor is the way to solve it! The GCF is 6, because it's the greatest number that evenly divided 12,24, and 30.
+26387 A store would like to set up fish tanks that contain equal numbers of angle fish, sword fish, and guppies.
What is the greatest number of tanks that can be set up if the store has 12 angle fish, 24 sword fish, and 30 guppies?
Formula:
\(\begin{array}{|rcll|} \hline \gcd(a,b,c) &=& \gcd( \gcd(a,b), c ) \\ \gcd(a,b ) &=& \gcd (a-b,b ) & a \ge b \\ \gcd(a,a) &=& a & a \ge 0 \\ \gcd(a,b) &=& \gcd(b,a) \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline \gcd(30,24,12) &=& \gcd( \gcd(30,24), 12 ) \\\\ && \gcd(30,24) \\ && = \gcd(30-24,24) \\ && = \gcd(6,24) \\ && = \gcd(24,6) \\ && = \gcd(24-6,6) \\ && = \gcd(18,6) \\ && = \gcd(18-6,6) \\ && = \gcd(12,6) \\ && = \gcd(12-6,6) \\ && = \gcd(6,6) \\ && = 6 \\\\ \gcd(30,24,12) &=& \gcd( \gcd(30,24), 12 ) \\\\ &=& \gcd( 6, 12 ) \\ &=& \gcd( 12, 6 ) \\ &=& \gcd( 12-6, 6 ) \\ &=& \gcd( 6, 6 ) \\ &=& 6 \\ \hline \end{array}\)
