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Use Euclid’s algorithm to find the HCF of 4052 and 12576.

Use Euclid’s algorithm to find the HCF of 4052 and 12576.

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2 Answers

Latika Leekha
askIITians Faculty 165 Points
8 years ago
Euclid’s Algorithm is a method of finding the G.C.D of two positive integers.
The algorithm states that the G.C.D of two positive integers is the largest integer that divides both of them without leaving a remainder.
Hence, using the algorithm we have,
12576 = 4052 . 3 + 420
We shall proceed this way until we obtain the remainder as zero.
4052 = 420.9 + 272
420 = 272.1 + 148
272 =148.1 + 124
124 = 4.6 + 0
Hence we have obtained the remainder as zero.
This shows that the H.C.F of 4052 and 12576 is 4.
Thanks & Regards
Latika Leekha
askIITians Faculty
Rishi Sharma
askIITians Faculty 646 Points
2 years ago
Dear Student,
Please find below the solution to your problem.

Euclid’s Algorithm is a method of finding the G.C.D of two positive integers.
The algorithm states that the G.C.D of two positive integers is the largest integer that divides both of them without leaving a remainder.
Hence, using the algorithm we have,
12576 = 4052 . 3 + 420
We shall proceed this way until we obtain the remainder as zero.
4052 = 420.9 + 272
420 = 272.1 + 148
272 =148.1 + 124
124 = 4.6 + 0
Hence we have obtained the remainder as zero.
This shows that the H.C.F of 4052 and 12576 is 4.

Thanks and Regards

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