Find the smallest natural number by which 2800 must be multiplied so that the product is perfect cube.
Answers
Answer:
980 is the answer of this question
The smallest number by which 2800 should be multiplied so that the product is a perfect square is 980.
Step-by-step explanation:
(1) First, we will find the prime factors of the number 2800.
2 | 2800
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2 | 1400
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2 | 700
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2 | 350
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5 | 175
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5 | 35
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7
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Prime factors of 2800 = 2 * 2* 2 * 2 * 5 * 5 * 7
In exponential form: 2³ * 2 * 5² * 7
(2) Now we have to multiply 2800 by a number so that its product is a perfect cube
Let the smallest number be “x”
Therefore,
2800 * x = 2³ * 2³ * 5³ * 7³
⇒ x = [2744000] / [2800]
⇒ x = 980 ← required smallest number
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