[br]In previous lessons, you've learned about prime factorization, prime and composite numbers, factors and multiples, and divisibility rules.[br][br][i][color=#0000ff]Climbing Down Trees:[/color][/i] https://www.geogebra.org/m/hxmuf2dg[br][i][color=#0000ff]Going Dutch:[/color][/i] https://www.geogebra.org/m/xvdee7pg[br][i][color=#0000ff]Sifting Grains:[/color][/i] https://www.geogebra.org/m/gamspcmt[br][br]In this lesson, we'll put these concepts together to find the [color=#0000ff]GREATEST COMMON FACTOR (GCF)[/color], also known as [color=#0000ff]GREATEST COMMON DIVISOR (GCD)[/color] or [color=#0000ff]HIGHEST COMMON FACTOR (HCF).[br][br][/color]The [color=#0000ff]GREATEST COMMON FACTOR (GCF)[/color] of two or more counting numbers is the greatest counting number that evenly divides all the given numbers. If that number is 1, then the two numbers are said to be [color=#0000ff]RELATIVELY PRIME.[/color] There are many approaches to finding the [color=#0000ff]GREATEST COMMON FACTOR[/color] or [color=#0000ff]GCF[/color]. The approach we'll use here will involve [color=#0000ff]PRIME FACTORIZATION[/color] of the numbers whose [color=#0000ff]GCF[/color] is being sought. The applet found in the lesson [color=#0000ff]Climbing Down Trees [/color]can be used here. The prime factors obtained there can be listed for all the numbers and the common factors identified. The number obtained by multiplying the common factors is the [color=#0000ff]GCF[/color].[br][br]Example: What is the GCF of 16 and 24?[color=#0000ff][br][br]Prime factors of 16 : [/color][color=#ff0000]2 x 2 x 2[/color][color=#0000ff] x 2[br]Prime factors of 24 : [/color][color=#ff0000]2 x 2 x 2[/color][color=#0000ff] x 3[br][br][/color]The [color=#0000ff]product[/color] of the common factors, [color=#ff0000]2 x 2 x 2[/color] (shown in [color=#ff0000]red[/color]) is the [color=#0000ff]GCF[/color], which is [color=#ff0000]8[/color].
[br]A [color=#0000ff]Venn Diagram[/color] can be used to visualize the concept of the [color=#0000ff]GCF[/color]. Using the example above, we can list the common prime factors of 16 and 24 inside the [color=#0000ff]lens[/color] (the [color=#0000ff]intersection[/color] of the two sets). The other prime factors are listed inside their respective [color=#0000ff]crescents[/color]. We now multiply the numbers inside the lens to find the [color=#0000ff]GCF[/color], which is [color=#ff0000]8[/color].
A more compact method of finding the GCF is through [color=#0000ff]CONTINUOUS DIVISION[/color] by prime factors, as illustrated below.[br][br][img]data:image/png;base64,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[/img][br]Start by dividing by the smallest common prime factor, and repeat the process until no common prime factor can be found. Multiply the common prime factors at the left side to find the [color=#0000ff]GCF[/color].[br][br]The [color=#0000ff]GCF[/color] is 2 x 2 x 2 or [color=#ff0000]8[/color].[br][br]Here's an example using three numbers.[br][br][img]data:image/png;base64,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[/img][br]The [color=#0000ff]GCF[/color] is 2 x 2 x 3 x 3 or [color=#ff0000]36[/color].[br][br]The process just discussed is the systematic way of finding the GCF. For bigger numbers, an [color=#0000ff]obviously[/color] common factor, [color=#ff7700]NOT NECESSARILY PRIME[/color], can be factored out first before the systematic process is applied. Consider this.[br][br][img]data:image/png;base64,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[/img][br]The [color=#0000ff]GCF[/color] is 10 x 2 x 3 x 7 or [color=#ff0000]420[/color].
Use the applet below for practice.[br][br]Enter 2 numbers in the entry boxes. Try solving the problem first on a separate sheet of paper, and then verify your answer by clicking [color=#6aa84f]Solutions[/color]. The GCF will appear below the numbers.[br][br]Click [color=#6aa84f]G.C.F. for 3 Numbers[/color] to work on 3 numbers, and follow the same procedure.[br][br]Repeat as many times as needed to master the concept.
In the next lesson, you're going to learn how to find the LEAST COMMON MULTIPLE. Did you ENJOY today's lesson?