find out the smallest number which when multiplied by the number which are not cube in question 1 give cube numbers
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1isthesmallest number
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Hint: In order to find the perfect cube of a number, write the prime factors of the number. If the prime factor occurs in multiple of 3, then the number is a perfect cube else it is not. If the prime factor is not forming a perfect cube then multiply by that prime number to make a number a perfect cube.
Complete step-by-step solution:
243
The prime factors of 243 are33×32.
Observing its factors it is clear that 243 can become a perfect cube by multiplying it with 3. After multiplication with 3, the number becomes 729 which is a perfect cube.
256
The prime factors of 256 are 23×23×22.
Observing its factors it is clear that 256 can become a perfect cube by multiplying it with 2. After multiplication with 3, the number becomes 512 which is a perfect cube.
72
The prime factors of 256 are23×32.
Observing its factors it is clear that 72 can become a perfect cube by multiplying it with 3. After multiplication with 3, the number becomes 216 which is a perfect cube.
675
The prime factors of 256 are33×52.
Observing its factors it is clear that 675 can become a perfect cube by multiplying it with 5. After multiplication with 5, the number becomes 3375 which is a perfect cube.
100
The prime factors of 100 are 22×52.
Observing its factors it is clear that in 100, there is a deficiency of one 2 and one 5, it can become a perfect cube by multiplying it with 2 and 5. After multiplying it with 2 and 5 or simply 10, the number becomes 1000 which is a perfect cube.