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Divide 5673375 by the smallest number so that the product is perfect cube.
- a)41
- b)43
- c)42
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Divide 5673375 by the smallest number so that the product is perfect c...
The Prime Factors are:
3 x 3 x 3 x 5 x 5 x 5 x 41 x 41
In Exponential Form:
33 x 53 x 412
So we have to divide by 41^2
Most Upvoted Answer
Divide 5673375 by the smallest number so that the product is perfect c...
To find the smallest number that can divide 5673375 and produce a perfect cube, we need to factorize 5673375 into its prime factors.
Prime factorization of 5673375:
5673375 = 3^2 * 5^3 * 13 * 41
From the prime factorization, we can see that the number 5673375 has factors of 3, 5, 13, and 41. To make the product a perfect cube, we need to divide by the smallest prime factor, which is 3.
Dividing 5673375 by 3:
5673375 / 3 = 1891125
Now, let's check if the product is a perfect cube.
Prime factorization of 1891125:
1891125 = 3^1 * 5^3 * 13 * 41
From the prime factorization, we can see that all the prime factors have a power of at least 3. Therefore, the product is indeed a perfect cube.
Hence, the smallest number that can divide 5673375 and produce a perfect cube is 3.
Therefore, the correct answer is option A) 41.
Prime factorization of 5673375:
5673375 = 3^2 * 5^3 * 13 * 41
From the prime factorization, we can see that the number 5673375 has factors of 3, 5, 13, and 41. To make the product a perfect cube, we need to divide by the smallest prime factor, which is 3.
Dividing 5673375 by 3:
5673375 / 3 = 1891125
Now, let's check if the product is a perfect cube.
Prime factorization of 1891125:
1891125 = 3^1 * 5^3 * 13 * 41
From the prime factorization, we can see that all the prime factors have a power of at least 3. Therefore, the product is indeed a perfect cube.
Hence, the smallest number that can divide 5673375 and produce a perfect cube is 3.
Therefore, the correct answer is option A) 41.
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Divide 5673375 by the smallest number so that the product is perfect cube.a)41b)43c)42d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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