Question

find the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube. i would mark the satisfactory answer as brainloest...plz help​

Answer 1

the smallest no. by which 1458 is divided by 2

Answer 2

2 is the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube

Solution:

Given,

We have to find the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube

STEP 1:

Find prime factorization of 1458

The Prime Factorization is:

$1458 = 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$

For a number to perfect cube, each of its prime factors must occur 3 times

Here, 2 occurs only one time

Thus,  1458 must be divided by 2 so that the quotient is a perfect cube

Check:

$\frac{1458}{2} = 729 = 9^3 = perfect\ cube$

Thus, 2 is the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube

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