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UKMT Junior Mathematical Olympiad, 2019

Number theory Difficulty 2.0 Junior Prove it United Kingdom

The number 3600 can be written as $2^{a} \times 3^{b} \times 4^{c} \times 5^{d}$ , where $a$ , $b$ , $c$ and $d$ are all positive integers. It is given that $a + b + c + d = 7$ . What is the value of $c$ ?

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