1188 = 2 × 2 × 3 × 3 × 3 × 11
The primes 2 and 11 do not appear in groups of three. So, 1188 is not a perfect cube. In the factorisation of 1188, prime 2 appears only two times and the prime 11 appears once. So, if we divide 1188 by 2 × 2 × 11 = 44, then the prime factorisation of the quotient will not contain 2 and 11.
Hence the smallest natural number by which 1188 should be divided to make it a
a perfect cube is 44.
And the resulting perfect cube is 1188 ÷ 44 = 27 [= 33].
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Question
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Is 1188 a perfect cube? If not, by which smallest natural number should 1188 be divided so that the quotient is a perfect cube?
Solution:
Thus, is not a perfect cube.
If we divide it by it will be a perfect cube.
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The smallest number with which 1188 should be divided to get a perfect cube is
Question
A
44
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B
54
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C
24
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Solution
The correct option is A 44
By prime factorisation,
311883396313224422211
1188=3×3×3×2×2×11
=33×22×11
=33×44
If we divide the given number by 44, the
resultant will be a perfect cube.
118844 = 27 =
33
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14
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