Question

Find the smallest number by which 2340 must be multiplied so that the product is a perfect cube

Answer 1

Hi there!
Here's the answer:


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¶¶¶ Type of problem :

To find the smallest No. by which a No. is to be multiplied so that the product is a perfect cube


¶¶¶ Approach to problem:

• Resolve the given No. into product of prime factors.
• Express the No. as product of prime factors in exponential form.
• The No. to be multiplied is the Prime No.(s) / factor(s) that do not have 3 as their power.

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SOLUTION:

Given,
No. = 2340

2 | 2340
2 | 1170
3 | 585
3 | 195
5 | 65
.• | 13

•°• The Prime Factorization is:
2 × 2 × 3 × 3 × 5 × 13

In Exponential Form
2340 = 2² × 3² × 5 × 13

To make product a perfect cube,
2340 has to be multiplied with 2×3×5²×13²= 25350

•°• Required No. to be multiplied = 25350.


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:)


Hope it helps

Answer 2

Heyaa!!☺
______________________
Given,
number is 2340.

The prime factors are 2,3,5,13.
Prime factorization is 2×2×3×3×13×5.
So,

=》The number to be multiplicated is 25350.
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Hope you understand...☺
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