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

To find the Highest Common Factor (HCF) of 4052 and 12576 using Euclid’s algorithm, we need to apply the division-based method.

Euclid’s algorithm is based on the principle that the HCF of two numbers also divides their difference. The steps are as follows:

Step 1: Divide the larger number by the smaller number and find the remainder.

12576 ÷ 4052 = 3 (quotient) with a remainder of 12576 - (3 × 4052) = 12576 - 12156 = 420.

Step 2: Now, take the divisor (4052) and divide it by the remainder (420).

4052 ÷ 420 = 9 (quotient) with a remainder of 4052 - (9 × 420) = 4052 - 3780 = 272.

Step 3: Now, take the divisor (420) and divide it by the remainder (272).

420 ÷ 272 = 1 (quotient) with a remainder of 420 - (1 × 272) = 420 - 272 = 148.

Step 4: Now, take the divisor (272) and divide it by the remainder (148).

272 ÷ 148 = 1 (quotient) with a remainder of 272 - (1 × 148) = 272 - 148 = 124.

Step 5: Now, take the divisor (148) and divide it by the remainder (124).

148 ÷ 124 = 1 (quotient) with a remainder of 148 - (1 × 124) = 148 - 124 = 24.

Step 6: Now, take the divisor (124) and divide it by the remainder (24).

124 ÷ 24 = 5 (quotient) with a remainder of 124 - (5 × 24) = 124 - 120 = 4.

Step 7: Now, take the divisor (24) and divide it by the remainder (4).

24 ÷ 4 = 6 (quotient) with a remainder of 0.

Step 8: When the remainder reaches 0, the divisor at this step (4) is the HCF of 4052 and 12576.

Therefore, the HCF of 4052 and 12576 is 4.