Solution: A number is a perfect cube only when each factor in the prime factorization of the given number exists in triplets. Using this concept, the smallest number can be identified. (i) 243  243 = 3 × 3 × 3 × 3 × 3 = 33 × 32 Here, one group of 3's is not existing as a triplet. To make it a triplet, we need to multiply by 3. Thus, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729 is a perfect cube Hence, the smallest natural number by which 243 should be multiplied to make a perfect cube is 3. (ii) 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 × 2 × 2 Here, one of the groups of 2’s is not a triplet. To make it a triplet, we need to multiply by 2. Thus, 256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 is a perfect cube Hence, the smallest natural number by which 256 should be multiplied to make a perfect cube is 2. (iii) 72 72 = 2 × 2 × 2 × 3 × 3 = 23 × 32 Here, the group of 3’s is not a triplet. To make it a triplet, we need to multiply by 3. Thus, 72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 = 216 is a perfect cube Hence, the smallest natural number by which 72 should be multiplied to make a perfect cube is 3. (iv) 675 675 = 5 × 5 × 3 × 3 × 3 = 52 × 33 Here, the group of 5’s is not a triplet. To make it a triplet, we need to multiply by 5. Thus, 675 × 5 = 5 × 5 × 5 × 3 × 3 × 3 = 3375 is a perfect cube Hence, the smallest natural number by which 675 should be multiplied to make a perfect cube is 5. (v) 100 100 = 2 × 2 × 5 × 5 = 22 × 52 Here both the prime factors are not triplets. To make them triplets, we need to multiply by one 2 and one 5. Thus, 100 × 2 × 5 = 2 × 2 × 2 × 5 × 5 × 5 = 1000 is a perfect cube Hence, the smallest natural number by which 100 should be multiplied to make a perfect cube is 2 × 5 =10 ☛ Check: NCERT Solutions for Class 8 Maths Chapter 7 Video Solution: NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1 Question 2 Summary: The smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.(i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100 are (i) 3, (ii) 2, (iii) 3, (iv) 5, and (v) 10 ☛ Related Questions:
Prime Factors of 14739 definition First note that prime numbers are all positive integers that can only be evenly divided by 1 and itself. Prime Factors of 14739 are all the prime numbers that when multiplied together equal 14739.How to find the Prime Factors of 14739 The process of finding the Prime Factors of 14739 is called Prime Factorization of 14739. To get the Prime Factors of 14739, you divide 14739 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1. This Prime Factorization process creates what we call the Prime Factor Tree of 14739. See illustration below.
How many Prime Factors of 14739? When we count the number of prime numbers above, we find that 14739 has a total of 4 Prime Factors. Product of Prime Factors of 14739 The Prime Factors of 14739 are unique to 14739. When you multiply all the Prime Factors of 14739 together it will result in 14739. This is called the Product of Prime Factors of 14739. The Product of Prime Factors of 14739 is: 3 × 17 × 17 × 17 = 14739Prime Factor Calculator Do you need the Prime Factors for a particular number? You can submit a number below to find the Prime Factors of that number with detailed explanations like we did with Prime Factors of 14739 above.Prime Factors of 14740 We hope this step-by-step tutorial to teach you about Prime Factors of 14739 was helpful. Do you want a test? If so, try to find the Prime Factors of the next number on our list and then check your answer here. Copyright | Privacy Policy | Disclaimer | Contact |
What is the smallest number by which 14739 must be divided so that the quotient is a perfect cube?
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