Find the smallest number by which 8788 must be divided to obtain a perfect cube
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So, in this pair of triplets, two 2 are extra. Therefore to get the perfect cube we have to divide the given number by 2×2, which is 4.
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Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now  iii Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube: 72 Solution 72 Prime factors of 72=2×2×2×3×3 Here 3 does not appear in 3’s group. Therefore, 72 must be multiplied by 3 to make it a perfect cube. 2722362182923 1Answer Verified Hint: We will use the Prime factorization method to solve this problem. Prime factorization is finding prime numbers which when multiplied, gave us the original number. Complete step-by-step answer: Given number is 8788. Now, we’ll do the prime factorization of 8788 \[8788 = 2 \times 2 \times 13 \times 13 \times 13 \] As we can see that the prime factor 2 doesn’t occur 3 times, so the given number is not a perfect cube. Hence, we will divide 8788 by 4$(2 \times 2)$ to get quotient as a perfect cube \[\Rightarrow \dfrac{8788}{4} = \dfrac{2\, \times\, 2\, \times\, 13\, \times\, 13\, \times\, 13}{4} \] \[\Rightarrow 2197 = 13 \times 13 \times 13 \] 2197 is a perfect cube. Therefore, the smallest number by which 8788 must be divided to get the quotient as a perfect cube is “4”. Note: A perfect cube is a number which is obtained on multiplying the same number thrice. A perfect square is a number which is obtained by multiplying the same number twice. Prime factorization is the process in which numbers will be broken down into sets of prime numbers which multiply together to result in the original number. The prime factorization method can be used to find the cube root of a number. The procedure is known as the prime factorization method because it entails resolving the integer whose cube root must be sought into its prime factors. We know that the powers of prime factors in a perfect cube are multiples of three. On prime factorizing the given number 8788, we have 8788 = 2 × 2 × 13 × 13 × 13 On grouping of the same kind of factors, it’s seen that 2 × 2 has been left ungrouping. 8788 = 2 × 2 × (13 × 13 × 13) So, 2 × 2 = 4 is the least number by which 8788 should be divided so that the quotient is a perfect cube. The prime factorization method can be used to find the cube root of a number. The procedure is known as the prime factorization method because it entails resolving the integer whose cube root must be sought into its prime factors. We know that the powers of prime factors in a perfect cube are multiples of three. On prime factorizing the given number 8788, we have 8788 = 2 × 2 × 13 × 13 × 13 On grouping of the same kind of factors, it’s seen that 2 × 2 has been left ungrouping. 8788 = 2 × 2 × (13 × 13 × 13) So, 2 × 2 = 4 is the least number by which 8788 should be divided so that the quotient is a perfect cube. What is the perfect cube of 8788?Hence, the smallest number by which 8788 must be multiplied to obtain a perfect cube is 2.
What is the smallest number by which 8748 must be divided to make it a perfect square?What is the smallest number by which 8748 must be divided to make it a perfect square? prime factors of 8748 are 2*2*3*3*3*3*3*3*3. After the prime factorisation there is one three left without a pair. So we should divide 8478 from 3,which is 2916.
What is the smallest number by which 3600 should be divided to get a perfect cube?3600 =24×32×52 In order to make it a perfect cube it has to be divided by 450.
What is the smallest number by which 675 must be multiplied to obtain a perfect cube?Hence, the smallest number by which 675 must be multiplied to obtain a perfect cube is 5.
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