Find the smallest number by which 16384 be divided so that the quotient may be a perfect cube

(i) 675 Prime factors of 675 = 3 × 3 × 3 × 5 × 5 = 3 3 × 5 2 We find that 675 is not a perfect cube. Hence, for making the quotient a perfect cube we divide it by 5 2 = 25, which gives 27 as quotient and we know that 27 is a perfect cube . (ii) 8640 Prime factors of 8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2 3 × 2 3 × 3 3 × 5 We find that 8640 is not a perfect cube. Hence, for making the quotient a perfect cube we divide it by 5 , which gives 1728 as quotient and we know that 1728 is a perfect cube. (iii) 1600 Prime factors of 1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 = 2 3 × 2 3 × 5 2 We find that 1600 is not a perfect cube. Hence, for making the quotient a perfect cube we divide it by 5 2 = 25, which gives 64 as quotient and we know that 64 is a perfect cube (iv) 8788 Prime factors of 8788 = 2 × 2 × 13 × 13 × 13 = 2 2 × 13 3 We find that 8788 is not a perfect cube. Hence, for making the quotient a perfect cube we divide it by 4, which gives 2197 as quotient and we know that 2197 is a perfect cube (v) 7803 Prime factors of 7803 = 3 × 3 × 3 × 17 × 17 = 3 3 × 17 2 We find that 7803 is not a perfect cube. Hence, for making the quotient a perfect cube we divide it by 17 2 = 289 , which gives 27 as quotient and we know that 27 is a perfect cube (vi) 107811 Prime factors of 107811 = 3 × 3 × 3 × 3 × 11 × 11 × 11 = 3 3 × 11 3 × 3 We find that 107811 is not a perfect cube. Hence, for making the quotient a perfect cube we divide it by 3, which gives 35937 as quotient and we know t...

2 3600 2 1800 2 900 2 450 3 225 3 75 5 25 5 5 1 Prime factors of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 Grouping the factors into triplets of equal factors, we get 3600 = 2 × 2 × 2 – –––––––– – × 2 × 3 × 3 × 5 × 5 We know that, if a number is to be a perfect cube, then each of its prime factors must occur thrice. We find that 2 occurs 4 times while 3 and 5 occurs twice only. Hence, the smallest number, by which the given number must be multiplied in order that the product is a perfect cube = 2 × 2 × 3 × 5 = 60 Also, product = 3600 × 60 = 216000 Now, arranging into triplets of equal prime factors, we have 216000 = 2 × 2 × 2 – –––––––– – × 2 × 2 × 2 – –––––––– – × 3 × 3 × 3 – –––––––– – × 5 × 5 × 5 – –––––––– – Taking one factor from each triplets, we get 3 √ 216000 = 2 × 2 × 3 × 5 = 60

The correct option is A 4 The given number, 16384's prime factorisation is : 2 16384 2 8192 2 4096 2 2048 2 1024 2 512 2 256 2 128 2 64 2 32 2 16 2 8 2 4 2 Therefore, 16384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2 3 × 2 3 × 2 3 × 2 3 × 2 2 ⇒If the number 16384 is divided by 2 2 = 4, the number obtained is = 2 3 × 2 3 × 2 3 × 2 3 which is a perfect cube ∴ Required number is 4.

Prime factorising, 2 5 9 8 7 5 = ( 3 × 3 × 3 ) × ( 5 × 5 × 5 ) × 7 × 1 1. We know, a perfect cube has multiples of 3 as powers of prime factors. Here, the prime factor 7 and 1 1 does not appear in triplet form. Therefore, 2 5 9 8 7 5 is not a perfect cube. Since in the factorization, 7 and 1 1 appears only one time, we must divide the number 2 5 9 8 7 5 by 7 × 1 1 = 7 7, then the quotient is a perfect cube. ∴ 2 5 9 8 7 5 ÷ 7 7 = 3 3 7 5 = 1 5 × 1 5 × 1 5 = 1 5 3, which is a perfect cube. ∴ The smallest number by which 2 5 9 8 7 5 should be divided to make it a perfect cube is 7 7.

Answer by Guest 4 is the smallest number in which 16384 can be divided so that the quotient may be a perfect cube. Given: 16384 To find: Find the smallest number by which 16384 can be divided so that the quotient may be perfect cube. Solution: The dividend of the question is 16384 The divisor of the question is X The property of the quotient is that it is a perfect square. Thereby, let start by taking out the prime factorization of 16384 which is Now as we can see that there are four which if multiplied will give a perfect cube but the number multiplied by those four is 4. 4 is the only number which is not a cube there by if we take out 4 from the factorization then the product of will be perfect cube. Hence if 16384 is divided by 4, then the quotient remaining is Therefore, the smallest number that can be divided to 16384 to give the quotient a perfect cube is 4. Mark as brainliest Answer by Guest Answer: The required number is 2. Step-by-step explanation: The given number is 16384. The prime factorization of this number is: Making pair of 3 2's, we get such 4 pairs. We are left with 2 × 2 Thus, we need to multiply the given number by 2 to make it a perfect cube. Cube root of the new obtained number is 32.

CBSE Study Material • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • RD Sharma Solutions for Class 8 Maths Chapter 4 – Cubes and Cube Roots are provided here. Chapter 4 – Cubes and Cube Roots contains five exercises, and the • Cube of a number – A natural number is said to be a perfect cube if it is a cube of some natural number • Finding a cube of a two-digit number by column method • Cubes of negative integers • Cubes of rational numbers • Cube root of a natural number • Cube root of a negative integral perfect cube • Cube root of the product of integers • Finding cube roots using cube root tables Previous Next Access Answers to RD Sharma Solutions for Class 8 Maths Chapter 4 – Cubes and Cube Roots EXERCISE 4.1 PAGE NO: 4.7 1. Find the cubes of the following numbers: (i) 7 (ii) 12 (iii) 16 (iv) 21 (v) 40 (vi) 55 (vii) 100 (viii) 302 (ix) 301 Solution: (i) 7 Cube of 7 is 7 = 7× 7 × 7 = 343 (ii) 12 The cube of 12 is 12 = 12× 12× 12 = 1728 (iii) 16 Cube of 16 is 16 = 16× 16× 16 = 4096 (iv) 21 Cube of 21 is 21 = 21 × 21 × 21 = 9261 (v) 40 The c...

You can . Divide 88209 by the smallest number so that the quotient is a perfect cube. What is that number ? Also find the cube root of the quotient ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 88209 = . Hence, your smallest number is , the quotient is = and the cube route of the quotient = 9.