what is the smallest number that should be multiplied to each of the following number to get a perfect cube 432 , 37044, 36864
Answers
Answer:
4
Step-by-step explanation:
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Answer:
Given number is 432
Writing 432
in prime factor from
(2) Therefore, prime factors of 432
are 2×2×2×3×3×3×2
=24×33
(3) Writing prime factor in group of three =24×33
(4) In the above step, we see that 2 is the only number which is not in the group of three.
Hence, we can say that 432
is not a perfect cube number.
(5) Now to make 432
as a perfect cube number, we should multiply it with such a number that it completes the three groups of elements of 2. (i.e. by 4)
(6) Therefore, on multiplying 432
by 4, we get prime factors as
=26×33
=23×23×33
=(2×2×3)3
=(12)3
=12×12×12
=1728
We see that all above prime factors are in a group of three elements. Hence, the number is a perfect cube.
(7) So, 4 is the least number by which 432
is to be multiplied to make it a perfect cube. 1728 is a perfect cube.