Asked by Dallas
Use the Euclidean Algorithm to find gcd(972, 1118).
Answers
Answered by
GPT 3.5
To find the greatest common divisor (gcd) of 972 and 1118 using the Euclidean Algorithm, we perform the following steps:
Step 1: Divide 1118 by 972
1118 = 972*1 + 146
Step 2: Now, divide the divisor (972) by the remainder (146)
972 = 146*6 + 96
Step 3: Next, divide the previous remainder (146) by the new remainder (96)
146 = 96*1 + 50
Step 4: Continue this process by dividing the previous remainder by the new remainder until we reach a remainder of 0
96 =50*1 + 46
50 =46*1 + 4
46 =4*11 + 2
4 =2*2 + 0
Step 5: The gcd(972, 1118) is the last non-zero remainder, which is 2.
Therefore, the gcd(972, 1118) is 2.
Step 1: Divide 1118 by 972
1118 = 972*1 + 146
Step 2: Now, divide the divisor (972) by the remainder (146)
972 = 146*6 + 96
Step 3: Next, divide the previous remainder (146) by the new remainder (96)
146 = 96*1 + 50
Step 4: Continue this process by dividing the previous remainder by the new remainder until we reach a remainder of 0
96 =50*1 + 46
50 =46*1 + 4
46 =4*11 + 2
4 =2*2 + 0
Step 5: The gcd(972, 1118) is the last non-zero remainder, which is 2.
Therefore, the gcd(972, 1118) is 2.