Question

Find by using Prime factorization whether
the following are perfect cubes?
13284


​

Answer 1

The number 13284 is not a perfect cube.

Step-by-step explanation:

• Prime factorization is the process of expressing a certain number as a product of prime factors or precisely, product of factors which are prime numbers.
• Here, the number given is 13284. Now, 13284 when divided by 2, gives, 6642, hence we got one prime factor that is 2.
• 6642 when divided by 2 gives, 3321. Hence, we got another prime factor that is 2. 6642 divided by 2 gives 3321. Hence, till now we got 2*2*2 which is a perfect cube. Now, 3321 when divided by 3 gives 1107. 1107 when divided by 3 gives 369. Again, 369 divided by 3 gives 123. 123 when divided by 3 gives 41.
• Since 41 is a single prime factor unlike 2 and 3 which has their frequency as perfect cubes.

Hence, the number 13284 is not a perfect cube.

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