Greatest Common Factor Directions: Find the GCF of exch of the fotiowng pars en murneters 1) \( 12 \quad 24 \) 2) \( 20 \quad 28 \) 3) \( 21 \quad 2 e \) 4) 924 5) 3243 6) \( 65 \quad 13 \) 7) \( 15 \quad 20 \) B) \( 54 \quad 60 \) 9) \( 3 \quad 21 \) (10) 4812 11) 4563 12) \( 40 \quad 120 \) 13) \( 90 \quad 20 \) 14) 2555 1511830 9 16) \( 22 \quad 26 \) 17) \( 108 \quad 36 \) 18) \( 42 \quad 14 \) 19) 628 20) 27 15 21) \( 24 \quad 32 \) 22) 5664 23) \( 36 \quad 60 \) \( 1+ \) 2 2 36 14 5 6 24
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Mind Expander
The concept of the greatest common factor (GCF) is rooted in the ancient Greeks' fascination with numbers. Euclid, the father of geometry, devised algorithms to determine such factors, laying the groundwork for what we now call the Euclidean algorithm. This historical tool helps us not only in mathematics but also in number theory, providing insights into the relationships between integers, making it a timeless classic! In real-world application, finding the GCF is useful in simplifying fractions, optimizing resources, and even in areas like music composition, where musicians might need to establish common rhythms. For instance, if two drumbeats occur at different intervals, determining the GCF can help align their patterns. So, whether you're cooking, composing, or constructing, GCF plays a surprising role in many aspects of life!
