Mẹo về Is 1188 a perfect cube if not by which smallest number should 1188 be divided to obtain a perfect cube? 2022

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288

1188 = 2 × 2 × 3 × 3 × 3 × 11

Nội dung chính

  • Is 1188 a perfect cube? If not, by which smallest natural number
    should 1188 be divided so that the quotient is a perfect cube?
  • Found the solution, but did not understand the concept?
  • The correct option is A 44By 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
  • Is 1188 a perfect cube if not by which smallest natural number should 1188?
  • Is 1188 a perfect cube if not then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?
  • What is the smallest number that must divide 1188 to make it a perfect cube?

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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24

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Solution

The correct option is A 44By 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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Is 1188 a perfect cube if not by which smallest natural number should 1188?

We see that 1188 = 2 × 2 × 3 × 3 × 3 × 11 Since 2 & 5 does not occur in triplets, ∴ 1188 is not a perfect cube. To make it a perfect cube, We divide by 2 × 2 × 11 = 44 1188/44= (2 × 2 × 3 × 3 × 3 × 11)/44 27 = 3 × 3 × 3 Since all factor occurs in triplets.

Is 1188 a perfect cube if not then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?

∴ The smallest number by which 53240 should be divided to make it a perfect cube is 5.

What is the smallest number that must divide 1188 to make it a perfect cube?

118844 = 27 = 33.
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