Question

By Euclid's Division Algorithm find the H.C.F. of 10540 and 7156
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Answer 1

Given numbers 10540 and 7156

10540 > 7156

We apply the division Lemma to 10540 and 7156

to get

10540 = 7156 × 1 + 3384

Now, consider division of 7156 with remainder 3384 and apply the division lemma to get

7156 = 3384 × 2 + 388

The remainder not equal to zero .so , apply the division lemma again

3384 = 388 × 8 + 280

388 = 280 × 1 + 108

280 = 108 × 2 + 64

108 = 64 × 1 + 44

64 = 44 × 1 + 20

44 = 20 × 2 + 4

20 = 4 × 5 + 0

The remainder has become zero so our procedure stops , Since the divisor at this stage is 4 .

Therefore.,

$\red{ H.C.F \: of \: 10540 \:and \: 7156} \green { = 4 }$

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