Prime factorisation of 1715 = 5*7*7*7
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Try the new Google Books Check out the new look and enjoy easier access to your favorite features (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. Try Numerade free for 7 days Try Numerade free for 7 days Continue
Try Numerade free for 7 days Try Numerade free for 7 days Continue Try Numerade free for 7 days Try Numerade free for 7 days Continue Prime factorisation of 1715 = 5*7*7*7 Scholr is India's Largest Knowledge Sharing Platform. Send Your Questions to Experts. Ask No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! |