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Use Euclid’s algorithm to find the H.C.F of 6265 and 76254

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 6265 and 76254,
We have to find H.C.F of the given terms by using Euclid’s algorithm,
Step 1= divided 76254 by 6265 and quotient is 12 and remainder is 1074.
76254=6265×12+1074
Step 2= remainder is not is not equal to 0, so again we divided 6265 by the first remainder is 1074 and we have a quotient is 5 and remainder is 895.
6265=1074×5+895
Step 3= remainder is not equal to zero, so again we divide 1075 by the second remainder 895 and we have a quotient of 1 and remainder is 179.
1075=895×1+179
Step 4= remainder is equal to zero. So we can stop our process here.
895=179×6+0

Hence, the Highest Common Factor (H.C.F) of numbers 76254 and 6265 is 179.

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 (a,b)=1 then we say that a and b 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 6265 and 76254,
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Hence, the Highest Common Factor (H.C.F) of numbers 76254 and 6265 is 179.
The Euclidean Algorithm for finding GCD (A,B) is as follows: If A=0 then the GCD (A,B)=B, since the GCD (0,B)=B, and we can stop. If B=0 then GCD (A,B)=A, since the GCD (A,0)=A and we can stop. Write A in quotient remainder from (A=B.Q+R).
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