Question

Find the smallest number which when multiplied with 26244 will make the product a perfect cube .Further find the cube root of the product

Answer 1

Hi there!
Here's the answer:

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¶ TYPE OF PROBLEM
To find the smallest No. which when multiplied with a No. will make the product a Perfect Cube

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¶ APPROACH TO PROBLEM :
• Resolve the Given No. into product of prime factors.
• Express them in exponential Form
• The product of Prime factor(s) which doesn't have 3 as their power is required smallest No.


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¶ SOLUTION:

Given,
No. = 26244

2 | 26244
2 | 13122
3 | 6561
3 | 2187
3 | 729
3 | 243
3 | 81
3 | 27
3 | 9
3 | 3
•. | 1

•°• 26244 = 2×2×3×3×3×3×3×3×3×3
=> 26244 = 3³ × 3² × 2²

Here the prime factors 3 and 2 aren't cubed.

•°• Required Least No. to be multiplied = 2×3 = 6

•°• The Perfect Cube = 26244×6 = 157464

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Hope it helps