AMC / AIME · Base Systems · Hard

Base Systems: Find the least base math such that math is divisible by math.

Convert and compute in bases.

Try the problem

Find the least base b>4b>4 such that (144)b(144)_b is divisible by 55.

Hint and answer

Concept to use

Arithmetic in base.

Hint

Expand place values or carry and borrow in the stated base.

Answer

8

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