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# Euclidean Algorithm

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Use the Euclidean Algorithm to find gcd(972, 1220).

Jun 20, 2024

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According to the Euclid's algorithm, we start with 2 numbers, a and b.

We do \(a ÷ b = c\) with remainder R where a is the larger of the two.

Then, we replace a with b and b with R, and do the same thing.

We repeat this prcoess until R is 0.

So, now we do the same with 972 and 1220.

\(1220 ÷ 972 = 1; R= 248\)

\(972 ÷ 248 = 3 ; R =228\)

\(248 ÷ 228 = 1 ;R= 20\)

\(228 ÷ 20 = 11 ;R= 8\)

\(20 ÷ 8 = 2 ;R =4\)

\(8 ÷ 4 = 2 ;R =0\)

When the remainder is 0, the GCF is the divisor. Thus, 4 is the GCF.

Thanks! :)

~NTS

Jun 20, 2024
edited by NotThatSmart  Jun 20, 2024

#1
+1230
+1

According to the Euclid's algorithm, we start with 2 numbers, a and b.

We do \(a ÷ b = c\) with remainder R where a is the larger of the two.

Then, we replace a with b and b with R, and do the same thing.

We repeat this prcoess until R is 0.

So, now we do the same with 972 and 1220.

\(1220 ÷ 972 = 1; R= 248\)

\(972 ÷ 248 = 3 ; R =228\)

\(248 ÷ 228 = 1 ;R= 20\)

\(228 ÷ 20 = 11 ;R= 8\)

\(20 ÷ 8 = 2 ;R =4\)

\(8 ÷ 4 = 2 ;R =0\)

When the remainder is 0, the GCF is the divisor. Thus, 4 is the GCF.