Question:
Find the remainder when (345672) in base 9 is divided by 8.
Find the remainder when (345672) in base 9 is divided by 8.
Updated On: Nov 17, 2025
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The Correct Option is C
Solution and Explanation
To begin with, let’s convert (345672)b to base 10.
= 2 × 90 + 7 × 91 + 6 × 92 + 5 × 93 + 4 × 94 + 3 × 95
Remainder \([\frac{2×9^0+7×9^1+6×9^2+5×9^3+4×9^4+3×9^4}{8}]\)
Remainder \([\frac{2×1^0+7×1^1+6×1^2+5×1^3+4×1^4+3×1^5}{8}]\)
Remainder \(\frac{[2+7+6+5+4+3]}{8}\) = Remainder \(\frac{27}{8}=3\)
So, the correct option is (C) : 3.
= 2 × 90 + 7 × 91 + 6 × 92 + 5 × 93 + 4 × 94 + 3 × 95
Remainder \([\frac{2×9^0+7×9^1+6×9^2+5×9^3+4×9^4+3×9^4}{8}]\)
Remainder \([\frac{2×1^0+7×1^1+6×1^2+5×1^3+4×1^4+3×1^5}{8}]\)
Remainder \(\frac{[2+7+6+5+4+3]}{8}\) = Remainder \(\frac{27}{8}=3\)
So, the correct option is (C) : 3.
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