
Use Euclid’s algorithm to find the H.C.F of and
Answer
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Hint: In this problem we are asked to find H.C.F of two numbers. Here H.C.F means Highest Common Divisor. When we find all the factors of given two numbers, and some factors are common, then the largest of those common factors is the greatest common factor. So let’s find the H.C.F of given two numbers.
Complete step-by-step solution:
The given terms and ,
We have to find H.C.F of the given terms by using Euclid’s algorithm,
Step divided by and quotient is and remainder is .
Step remainder is not is not equal to , so again we divided by the first remainder is and we have a quotient is and remainder is .
Step remainder is not equal to zero, so again we divide by the second remainder and we have a quotient of and remainder is .
Step remainder is equal to zero. So we can stop our process here.
Hence, the Highest Common Factor (H.C.F) of numbers and is .
Additional Information: The Euclidean algorithm, or Euclid’s algorithm, is an efficient method for computing the greatest common divisor of two integers, the largest number that divides them both without a remainder. If G.C.D then we say that and are co-prime or relatively prime. It is named after the ancient Greek mathematician Euclid, who first described it in his elements.
Note: We can solve this problem by tree factorization method,
The given terms and ,
Hence, the Highest Common Factor (H.C.F) of numbers and is .
The Euclidean Algorithm for finding GCD is as follows: If then the GCD , since the GCD , and we can stop. If then GCD , since the GCD and we can stop. Write A in quotient remainder from .
Complete step-by-step solution:
The given terms
We have to find H.C.F of the given terms by using Euclid’s algorithm,
Step
Step
Step
Step
Hence, the Highest Common Factor (H.C.F) of numbers
Additional Information: The Euclidean algorithm, or Euclid’s algorithm, is an efficient method for computing the greatest common divisor of two integers, the largest number that divides them both without a remainder. If G.C.D
Note: We can solve this problem by tree factorization method,
The given terms

Hence, the Highest Common Factor (H.C.F) of numbers
The Euclidean Algorithm for finding GCD
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