Explanation:
To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:
Step 1: Apply Euclid's division lemma:
Divide the larger number, 567, by the smaller number, 255, and find the remainder.
567 ÷ 255 = 2 remainder 57
Step 2: Apply Euclid's division lemma again:
Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.
255 ÷ 57 = 4 remainder 27
Step 3: Repeat the process:
Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.
57 ÷ 27 = 2 remainder 3
Step 4: Continue until we obtain a remainder of 0:
Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.
27 ÷ 3 = 9 remainder 0
Since we have obtained a remainder of 0, the process ends here.
Step 5: The H.C.F. is the last non-zero remainder:
The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.
Therefore, the H.C.F. of 567 and 255 is 3.