Question

Find HCF the 4052 and 12576 using Euclid's algorithm​

Answer 1

Answer:

According to the definition of Euclid's theorem,

a = b × q + r where 0 ≤ r < b.

Using euclid's  algorithm

12576=4052×3+420

4052=420×9+272

420=272×1+148

272=148×1+124

124=24×5+4

24=4×6+0

Therefore 4 is the H.C.F of 4052 and 12576

Step-by-step explanation:

Answer 2

Answer:

4 IS THE HCF

Step-by-step explanation:

Here 12576 is greater than 4052

Now, consider the largest number as 'a' from the given number ie., 12576 and 4052 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 12576 > 4052, we apply the division lemma to 12576 and 4052, to get

12576 = 4052 x 3 + 420

Step 2: Since the reminder 4052 ≠ 0, we apply division lemma to 420 and 4052, to get

4052 = 420 x 9 + 272

Step 3: We consider the new divisor 420 and the new remainder 272, and apply the division lemma to get

420 = 272 x 1 + 148

We consider the new divisor 272 and the new remainder 148,and apply the division lemma to get

272 = 148 x 1 + 124

We consider the new divisor 148 and the new remainder 124,and apply the division lemma to get

148 = 124 x 1 + 24

We consider the new divisor 124 and the new remainder 24,and apply the division lemma to get

124 = 24 x 5 + 4

We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get

24 = 4 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4052 and 12576 is 4

Notice that 4 = HCF(24,4) = HCF(124,24) = HCF(148,124) = HCF(272,148) = HCF(420,272) = HCF(4052,420) = HCF(12576,4052) .

Therefore,  THE HCF of 4052,12576 using Euclid's division lemma is 4.

I HOPE YOU UNDERSTOOD THE QUESTION!!!