Question
Mathematics Question on Number Systems
The remainder when 4282024 is divided by 21 is __________.
Step 1: Simplify 4282024mod21 Write 428 as:
428=420+8.
Thus:
4282024=(420+8)2024.
When divided by 21, 420 is a multiple of 21:
4282024≡82024(mod21).
Step 2: Simplify 82024mod21 Write 82024 as:
82024=(82)1012.
Calculate 82:
82=64.
Thus:
82024≡641012(mod21).
Step 3: Simplify 64mod21 Since 64=63+1=21×3+1, we have:
64≡1(mod21).
Thus:
641012≡11012(mod21).
Step 4: Final Result
82024≡1(mod21).
Hence, the remainder when 4282024 is divided by 21 is: 1.
Solution
Step 1: Simplify 4282024mod21 Write 428 as:
428=420+8.
Thus:
4282024=(420+8)2024.
When divided by 21, 420 is a multiple of 21:
4282024≡82024(mod21).
Step 2: Simplify 82024mod21 Write 82024 as:
82024=(82)1012.
Calculate 82:
82=64.
Thus:
82024≡641012(mod21).
Step 3: Simplify 64mod21 Since 64=63+1=21×3+1, we have:
64≡1(mod21).
Thus:
641012≡11012(mod21).
Step 4: Final Result
82024≡1(mod21).
Hence, the remainder when 4282024 is divided by 21 is: 1.