+0  
 
0
1
1
avatar+721 

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

 Jun 20, 2024

Best Answer 

 #1
avatar+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. 

So our answer is 4. 

 

Thanks! :)

 

~NTS

 Jun 20, 2024
edited by NotThatSmart  Jun 20, 2024
 #1
avatar+1230 
+1
Best Answer

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. 

So our answer is 4. 

 

Thanks! :)

 

~NTS

NotThatSmart Jun 20, 2024
edited by NotThatSmart  Jun 20, 2024

2 Online Users

avatar