Find the smallest number by which 182250 be divided so that a quotient becomes a perfect cube
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Prime factorising 18522, we get,
18522=2×3×3×3×7×7×7
=2
1
×3
3
×7
3
.
We know, a perfect cube has multiples of 3 as powers of prime factors.
Here, number of 2's is 1, number of 3's is 3 and number of 7's is 3.
So we need to divide 2 from the factorization to make 18522 a perfect cube.
Hence, the smallest number by which 18522 must be divided to obtain a perfect cube is 2.
hope this helps
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