Use Euclid’s division algorithm to find the HCF of 441, 567, 693.
63
Step 1: Recall Euclid’s Division Algorithm.
For any two positive integers \(a\) and \(b\), with \(a > b\), we can write:
\(a = bq + r\), where \(0 \leq r < b\).
If \(r = 0\), then \(b\) is the HCF of \(a\) and \(b\). Otherwise, repeat the process with \(b\) and \(r\).
Step 2: Find HCF of 567 and 441.
Divide 567 by 441:
\(567 = 441 \times 1 + 126\)
Now divide 441 by 126:
\(441 = 126 \times 3 + 63\)
Now divide 126 by 63:
\(126 = 63 \times 2 + 0\)
Since remainder is 0, the HCF of 567 and 441 is 63.
Step 3: Find HCF of 693 and 63.
Divide 693 by 63:
\(693 = 63 \times 11 + 0\)
So, the HCF of 693 and 63 is 63.
Step 4: Combine results.
Hence, the HCF of 441, 567, and 693 is 63.