Using Euclid's Algorithm to Find the Highest Common Factor (HCF)

Question 1: Finding the HCF of 1320 and 935

To find the HCF of two numbers using Euclid's algorithm, we follow these steps:

Step 1: Divide the larger number by the smaller number.
In this case, 1320 ÷ 935 = 1 with a remainder of 385.

Step 2: Now, divide the smaller number (935) by the remainder (385).
935 ÷ 385 = 2 with a remainder of 165.

Step 3: Repeat the process until the remainder becomes zero.
385 ÷ 165 = 2 with a remainder of 55.
165 ÷ 55 = 3 with a remainder of 0.

Since the remainder has become zero, we stop here.

Step 4: The divisor of the last non-zero remainder (55) is the HCF of the given numbers.
Therefore, the HCF of 1320 and 935 is 55.

Question 2: Finding the HCF of 1624 and 1276

Step 1: Divide the larger number by the smaller number.
In this case, 1624 ÷ 1276 = 1 with a remainder of 348.

Step 2: Now, divide the smaller number (1276) by the remainder (348).
1276 ÷ 348 = 3 with a remainder of 232.

Step 3: Repeat the process until the remainder becomes zero.
348 ÷ 232 = 1 with a remainder of 116.
232 ÷ 116 = 2 with a remainder of 0.

Since the remainder has become zero, we stop here.

Step 4: The divisor of the last non-zero remainder (116) is the HCF of the given numbers.
Therefore, the HCF of 1624 and 1276 is 116.

Conclusion:
Using Euclid's algorithm, we can find the HCF of two numbers by repeatedly dividing the larger number by the smaller number and the smaller number by the remainder until the remainder becomes zero. The divisor of the last non-zero remainder is the HCF of the given numbers. In the case of 1320 and 935, the HCF is 55, and in the case of 1624 and 1276, the HCF is 116.