Octal of 1729 decimal – UGC NET Question

Using repeated division of 1729 by 8 gives remainders that form the octal digits 3, 3, 0 and 1 from most significant to least significant. Thus the correct octal form is 3301₈. Expanding 3301₈ as 3×8³ + 3×8² + 0×8¹ + 1×8⁰ yields 1536 + 192 + 0 + 1 = 1729. This confirms that 3301 is the correct octal representation.

Option A:
3231₈ expands to 3×512 + 2×64 + 3×8 + 1 = 1536 + 128 + 24 + 1 = 1689. Since 1689 is less than 1729, this octal number cannot represent the given decimal value. It is a reasonable distractor but numerically wrong.

Option B:
3301₈ evaluated as 3×512 + 3×64 + 0×8 + 1 gives 1536 + 192 + 0 + 1 = 1729. This matches the target decimal exactly, demonstrating a correct conversion. The pattern of digits and place values reflects proper repeated division by eight.

Option C:
3401₈ gives 3×512 + 4×64 + 0×8 + 1 = 1536 + 256 + 0 + 1 = 1793. Because 1793 is greater than 1729, it overshoots the required value. Thus, it cannot be the correct conversion.

Option D:
3310₈ represents 3×512 + 3×64 + 1×8 + 0 = 1536 + 192 + 8 + 0 = 1736. As 1736 is slightly above 1729, this octal number is again not the exact representation. It shows how sensitive the last digit is in positional systems.