Thus $ 52500 \equiv 8 + 4 = 12 \pmod{16} $
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- First, $ 1000 \equiv 8 \pmod{16} $, so $ 5000 = 5 \cdot 1000 \equiv 5 \cdot 8 = 40 \equiv 8 \pmod{16} $ (since $ 40 - 2 \cdot 16 = 8 $)
- Then $ 52500 = 5000 + 500 = 8 + 500 $
- Now $ 500 \div 16 $: $ 16 \cdot 31 = 496 $, so $ 500 \equiv 4 \pmod{16} $
- Alternatively, divide directly:
- $ 52500 \div 16 = 3281.25 $, but compute:
- $ 16 \cdot 3281 = 16 \cdot 3000 = 48000 $, $ 16 \cdot 281 = 4496 $, total $ 48000 + 4496 = 52496 $
