Question

use Euclid's algorithm to find the HCF of 4052 and 12576​

Answer 1

Step-by-step explanation:

Euclid's algorithm states that , for any two integers a and b such that a>b, if we can write,

a=bq+r, where q is quotient and r is remainder, then,

HCF(a,b)=HCF(q,r)

In our case, a=12576 and b=4052

12576=4052∗3+420

So, HCF(12576,4052)=HCF(4052,420)

Similarly,

4052=420∗9+272

420=272∗1+148

272=148∗1+124

148=124∗1+24

124=24∗5+4

24=4∗6+0

So, HCF(12576,4052)=HCF(24,4)=4

Answer 2

Step-by-step explanation:

According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.

HCF is the largest number which exactly divides two or more positive integers.

Since 12576 > 4052

12576 = (4052 × 3) + 420

420 is a reminder which is not equal to zero (420 ≠ 0).

4052 = (420 × 9) + 272

271 is a reminder which is not equal to zero (272 ≠ 0).

Now consider the new divisor 272 and the new remainder 148.

272 = (148 × 1) + 124

Now consider the new divisor 148 and the new remainder 124.

148 = (124 × 1) + 24

Now consider the new divisor 124 and the new remainder 24.

124 = (24 × 5) + 4

Now consider the new divisor 24 and the new remainder 4.

24 = (4 × 6) + 0

Reminder = 0

Divisor = 4

HCF of 12576 and 4052 = 4.