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

priya , 11 Years ago

Grade

2 Answers

Latika Leekha

Last Activity: 10 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

Last Activity: 4 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