Use Euclid's division algorithm to find the HCF of 441, 567, 693.

To find the Highest Common Factor (HCF) of the numbers 441, 567, and 693 using Euclid's division algorithm, we will follow a systematic approach.

Step 1: Find HCF of the First Two Numbers

First, we calculate the HCF of 441 and 567.

Calculating HCF(441, 567)

We apply the division algorithm:

• Divide 567 by 441:

567 ÷ 441 = 1 (remainder 126)

So, we write:

567 = 441 × 1 + 126

• Now, we find HCF(441, 126):

Divide 441 by 126:

441 ÷ 126 = 3 (remainder 63)

Thus:

441 = 126 × 3 + 63

• Next, we find HCF(126, 63):

Divide 126 by 63:

126 ÷ 63 = 2 (remainder 0)

So:

126 = 63 × 2 + 0

Since the remainder is 0, we have:

HCF(441, 567) = 63

Step 2: Find HCF of the Result with the Third Number

Now, we need to find HCF(63, 693).

Calculating HCF(63, 693)

Using the division algorithm again:

• Divide 693 by 63:

693 ÷ 63 = 11 (remainder 0)

Thus:

693 = 63 × 11 + 0

Since the remainder is 0, we conclude:

HCF(63, 693) = 63

Final Result

The Highest Common Factor of 441, 567, and 693 is 63.