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Number Theory Level 2

What is the smallest positive integer to be multiplied to 775 so that the resulting product is a perfect cube?


The answer is 4805.

Brian Dela Torre by Brian Dela Torre , 21, Philippines

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1 solution

Brian Dela Torre
Jan 31, 2016

Since 775 = 5 2 × 31 5^{2}\times 31 , we will multiply 5 × 3 1 2 5\times 31^{2} to make it 5 3 × 3 1 3 5^{3}\times 31^{3} which is the smallest possible perfect cube,

Hence 5 × 3 1 2 5\times 31^{2} = 4805 \boxed{4805}

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