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∴ 625 = 5 × 5 × 5 × 5 = 53 × 5For the smallest cube number,625 should be divided 5, 625 ÷ 5 = 125 = 53
(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.
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What is the smallest positive integer by which 625 must be divided so [#permalink]
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Question Stats: Hide Show timer StatisticsWhat is the smallest positive integer by which 625 must be divided so that the quotient is a perfect cube?(A) 125 (B) 25(C) 5(D) 3 (E) 2 _________________
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Re: What is the smallest positive integer by which 625 must be divided so [#permalink] Option: CPrime factorization of 625 is625 = 5 × 5 × 5 × 5As seen above the smallest prime factor is 5Here a perfect cube would be 5 x 5 x 5 = 125Therefore 5 is the smallest positive integer by which 625 must be divided to get a perfect cube as a quotient. Posted from my mobile device
Re: What is the smallest positive integer by which 625 must be divided so [#permalink] 30 Aug 2022, 04:48 Description for Correct answer: 5 | 625 5 | 125 5 | 25 5 | 5 | 1\( \Large 625 = 5 \times 5 \times 5 \times 5 \) Smallest number = 5 Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification Comments Similar Questions |