Find the smallest number by which the following must be divided to make them the perfect cube 5324
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(i)81 Prime factors of 81 = 3\times3\times3\times3 Here one factor 3 is not grouped in triplets. Therefore 81 must be divided by 3 to make it a perfect cube. (ii) 128 Prime factors of 128 = 2\times2\times2\times2\times2\times2 Here one factor 2 does not appear in a 3’s group. Therefore, 128 must be divided by 2 to make it a perfect cube. (iii) 135 Prime factors of 135 = 3\times3\times3\times5 Here one factor 5 does not appear in a triplet. Therefore, 135 must be divided by 5 to make it a perfect cube. (iv) 192 Prime factors of 192 = 2\times2\times2\times2\times2\times3 Here one factor 3 does not appear in a triplet. Therefore, 192 must be divided by 3 to make it a perfect cube. (v) 704 Prime factors of 704 = 2\times2\times2\times2\times2\times2\times11 Here one factor 11 does not appear in a triplet. Therefore, 704 must be divided by 11 to make it a perfect cube. (i) We have, 1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 After grouping the prime factors in triplets, it’s seen that one factor 3 is left without grouping. 1536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3 So, in order to make it a perfect cube, it must be divided by 3. Thus, the smallest number by which 1536 must be divided to obtain a perfect cube is 3. (ii) We have, 10985 = 5 × 13 × 13 × 13 After grouping the prime factors in triplet, it’s seen that one factor 5 is left without grouping. 10985 = 5 × (13 × 13 × 13) So, it must be divided by 5 in order to get a perfect cube. Thus, the required smallest number is 5. (iii) We have, 28672 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 After grouping the prime factors in triplets, it’s seen that one factor 7 is left without grouping. 28672 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 7 So, it must be divided by 7 in order to get a perfect cube. Thus, the required smallest number is 7. (iv) 13718 = 2 × 19 × 19 × 19 After grouping the prime factors in triplets, it’s seen that one factor 2 is left without grouping. 13718 = 2 × (19 × 19 × 19) So, it must be divided by 2 in order to get a perfect cube. Thus, the required smallest number is 2. Open in App Solution 2×2×11×11×11=5324 so the smallest natural number should 5324 be divided so that the quotient is a perfect cube is 2×2=4 Ans: 4Similar questions Q. By what least number should 1536 be divided to get a perfect cube? Q. Find the least number by which
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How do you find the smallest number to be divided to get a perfect cube?Prime factorising 81, we get,. We know, a perfect cube has multiples of 3 as powers of prime factors.. Here, number of 3's is 4.. So we need to divide the factorization by 3 to make 81 a perfect cube.. Hence, the smallest number by which 81 must be divided to obtain a perfect cube is 3.. Is 5324 a perfect cube give reason to support your answer?Since 2 does not occur in triplets. ∴ 5324 is not a perfect cube.
Which is the smallest number by which 5324 is multiplied so that the product is a perfect cube?Answer: We have to multiply the given number by 2 to make a perfect cube. Step-by-step explanation: The given number is 5324.
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