Question

with what least number must 8640 be divided so that the quotient is a perfect cube ​

Answer 1

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with what least number must 8640 be divided so that the quotient is a perfect cube

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This question can be done easily by prime factorization method

• In order to find the smallest number to be divided first we factorize 8640.
• ⇒8640=2×2×2×2×2×2×3×3×3×5⇒8640=26×33×5
• In the above factorization, we find that there is a triplet of 2 and 3 but there is no triplet of 5.
• Hence, 5 is the smallest number which must divide 8640 so that the quotient is a perfect cube.
• Note: Any number which is a perfect cube will be multiple of a triplet of digits. Cube roots of the number can also be found out by the above mentioned prime factorization method.

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