Question

Smallest number that maltiplied tomake 142884 a perfect cube

Answer 1

Question

Find the smallest number that can be multiplied to 142884 to obtain a perfect cube.

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Answer

First we'll prime factorize 142884.

$\begin{array}{r | l} 2 & 142884 \\ \cline{2-2} 2 & 71442 \\ \cline{2-2} 3 & 35721 \\ \cline{2-2} 3 & 11907 \\ \cline{2-2} 3 & 3969 \\ \cline{2-2} 3 & 1323 \\\cline{2-2} 3&441 \\ \cline{2-2} 3& 147 \\\cline{2-2} 7& 49\\ \cline{2-2} & 7 \\ \end{array}$

142884 ⇒ 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7

Now we shall group the product of primes in groups of 3 in each.

142884 ⇒ 2 × 2 × (3 × 3 × 3) × (3 × 3 × 3) × 7 × 7

Here we need 2 and 7 to complete the groups so we must multiply 14 (2×7) to 142884 to obtain a perfect square.

142884 × 2 × 7 ⇒ 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7 × 7

2000376 ⇒ (2 × 2 × 2) × (3 × 3 × 3) × (3 × 3 × 3) × (7 × 7 × 7)

∴ We must multiply 14 to 142884 to obtain a perfect cube.

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Answer 2

Answer:

14

Step-by-step explanation:

142884 ⇒ 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 × 7 × 7

2 and 7 are not in a pair.

2 X 7 = 14 .

So 14 is the required number