Question

The HCF of 306 and 657 is

• A. 10
• B. 8
• C. 9
• D. 7

Answer 1

The Correct Option is C

To find the HCF of 306 and 657, we'll use the Euclidean algorithm:

Step 1: Apply division algorithm to 657 and 306

\( 657 = 306 \times 2 + 45 \)

Step 2: Now apply division algorithm to 306 and 45

\( 306 = 45 \times 6 + 36 \)

Step 3: Apply division algorithm to 45 and 36

\( 45 = 36 \times 1 + 9 \)

Step 4: Apply division algorithm to 36 and 9

\( 36 = 9 \times 4 + 0 \)

Since the remainder is now 0, the HCF is the last non-zero remainder.

Conclusion

The HCF of 306 and 657 is (3) 9.