Question

use the euclidean algorithm to find gcd (1001,1331)

Answer 1

1331=1001*1+330

1331=1001*1+3301001=330*3+11

1331=1001*1+3301001=330*3+11330=11*30+0

1331=1001*1+3301001=330*3+11330=11*30+0Therefore 11 is the greatest common divisor. Notice that each remainder has the gcd as a factor-which is the sole proof of the Euclidean algorithm. It will be the last factor before you arrive at 0.

1331=1001*1+3301001=330*3+11330=11*30+0Therefore 11 is the greatest common divisor. Notice that each remainder has the gcd as a factor-which is the sole proof of the Euclidean algorithm. It will be the last factor before you arrive at 0.Another method is to take the intersection of the prime factorization of each number.

1331=1001*1+3301001=330*3+11330=11*30+0Therefore 11 is the greatest common divisor. Notice that each remainder has the gcd as a factor-which is the sole proof of the Euclidean algorithm. It will be the last factor before you arrive at 0.Another method is to take the intersection of the prime factorization of each number.1331=11^3 and 330=11*2*5

1331=1001*1+3301001=330*3+11330=11*30+0Therefore 11 is the greatest common divisor. Notice that each remainder has the gcd as a factor-which is the sole proof of the Euclidean algorithm. It will be the last factor before you arrive at 0.Another method is to take the intersection of the prime factorization of each number.1331=11^3 and 330=11*2*5Since they only have 11 in common(the intersection) it is the gcd.

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