4. What is the
5. Write cubes of five natural numbers which are multiples of 3 and verify the following
The cube of a natural number which is a multiple of 3 is a multiple of 27'.
prime factorisation method:
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Answer:
Five natural numbers, which are multiples of 3, are 3, 6, 9, 12 and 15.
Step-by-step explanation:
Cubes of these five numbers are:
33 = 3 x 3 x 3 = 27
63 = 6 x 6 x 6 = 216
93 = 9 x 9 x 9 = 729
123 = 12 x 12 x 12 = 1728
153 = 15 x 15 x 15 = 3375
Now, let us write the cubes as a multiple of 27. We have:
27 = 27 x 1
216 = 27 x 8
729 = 27 x 27
1728 = 27 x 64
3375 = 27 x 125
It is evident that the cubes of the above multiples of 3 could be written as multiples of 27. Thus, it is verified that the cube of a natural number, which is a multiple of 3, is a multiple of 27.
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